This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz...This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the glob...In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.展开更多
Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we pro...Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.展开更多
In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are cont...In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.展开更多
The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J.E.Dunn and J.Serrin(1985),in the case of van der Waals ga...The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J.E.Dunn and J.Serrin(1985),in the case of van der Waals gas.Under the small initial perturbation,the proof of the global existence is based on an elementary energy method using the continuation argument of local solution.Moreover,the uniqueness of global solutions and large time behavior of the density are given.It is one of the main difficulties that the pressure p is not the increasing function of the densityρ.展开更多
Asphaltenes are the most elusive substances in waxy crude oil,especially the complex structures,which leads to significant precipitation and aggregation characteristics of asphaltenes,and affects the asphaltenes-wax i...Asphaltenes are the most elusive substances in waxy crude oil,especially the complex structures,which leads to significant precipitation and aggregation characteristics of asphaltenes,and affects the asphaltenes-wax interaction.In this study,the concept of the existence state of asphaltenes was introduced to semi-quantitatively investigate the precipitation and aggregation characteristics of asphaltenes.On this basis,the influence of the existence state of asphaltenes on wax deposition was studied by coldfinger device and high-temperature gas chromatography,and the composition and properties of the deposits were analyzed.Four main findings were made:(1)As the asphaltene concentration increases,the existence state of asphaltenes gradually transitions from dispersed state to aggregated state,and the asphaltene concentration of 0.30 wt%in this study is the starting point of the transition.(2)The existence state of asphaltenes in crude oil does affect the process of wax deposition,as shown in the fact that the dispersed asphaltenes promote the occurrence of wax deposition,while the aggregated asphaltenes can inhibit wax deposition.(3)In the presence of the aggregated asphaltenes,that is,when the asphaltene concentration is higher than 0.30 wt%,the shedding phenomenon of deposit layer was observed,and with the increase of aggregated asphaltenes,the deposit layer fell off earlier.(4)With the increase of the dispersed asphaltenes,the wax appearance temperature(WAT)and wax content of the deposits all showed an increasing trend,while with the appearance of the aggregated asphaltenes,the above situation was reversed.The findings of this study can help for better understanding of the interaction between the asphaltenes and wax in wax deposition.展开更多
In this paper,we focus on a general n-dimension system of k-Hessian equations.By introducing some new suitable growth conditions,the existence results of radial k-admissible solutions of the k-Hessian system are obtai...In this paper,we focus on a general n-dimension system of k-Hessian equations.By introducing some new suitable growth conditions,the existence results of radial k-admissible solutions of the k-Hessian system are obtained.Our approach is largely based on the well-known fixed-point theorem.展开更多
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri...In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.展开更多
This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial da...This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).展开更多
The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have stud...The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.展开更多
In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differen...In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.展开更多
Any journalist would consider it a career highlight to cover a major historical event or witness a ground-breaking breakthrough.I am thankful that the milestone 20th National Congress of the Communist Party of China (...Any journalist would consider it a career highlight to cover a major historical event or witness a ground-breaking breakthrough.I am thankful that the milestone 20th National Congress of the Communist Party of China (CPC) came as a fortuitous stroke of serendipity in my professional life.展开更多
[Objectives]To explore the evolution of the legal system of farmland protection and explore the rules and characteristics of policy development based on the theory and logic of institutional change since China's r...[Objectives]To explore the evolution of the legal system of farmland protection and explore the rules and characteristics of policy development based on the theory and logic of institutional change since China's reform and opening up,reveal the problems and deep-seated reasons of its legislation,clarify the direction of farmland protection in the new period,and solve the"non-agricultural""non-grain"and ecological problems of farmland.[Methods]Literature analysis and inductive deduction methods were used.[Results]The evolution of the farmland protection legal system has gone through the process of"national consciousness-policy guidelines-institutional system",the change from"single subject to multiple subjects";change from the use of"one-way administrative means to coordinated use of administrative,economic and technical means".The practical problems of the farmland protection legal system are mainly due to the insufficient systematization of the farmland protection legal system itself,the generalization of quantity protection,the transformation of quality protection,and the absence of ecological protection.[Conclusions]It is recommended to improve the existing farmland protection legal system from the establishment of the Farmland Protection Law,the improvement of the farmland protection public participation mechanism and supervision mechanism,the establishment of the farmland quality construction and improvement system,the differentiated farmland occupation and supplementation balance system,and the ecological restoration system.展开更多
托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantu...托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantum esse,being as beinginjeneral)。他在论证是自身时强调实在意义上的是重于逻辑意义的是。是(being)包括本质(essence)与存在(existence);本质(essence)与存在(existence)皆为是者(beings)。而存在(existence)先于本质(essence);存在(existence)是是(being)之最具体的、个别的、实体的、独一无二的完美实现(act)。托马斯.阿奎那的存在论哲学颠覆了传统哲学中存在与本质的位置,它以一种存在主义代替本质主义,从而在形而上学历史上掀起一场革命。展开更多
China English is an objective existence as a performance variety used in China.It is based on standard English and possesses Chinese characteristics.The Chinese characteristics of China English are reflected in the ph...China English is an objective existence as a performance variety used in China.It is based on standard English and possesses Chinese characteristics.The Chinese characteristics of China English are reflected in the phonology,vocabulary,syntax,rhetoric and text,particularly in the vocabulary.This essay will discuss the features of China English from the following three aspects: the development of English in China;the comparison between China English,Pidgin English and Chinese English and the Chinese words borrowed by English.展开更多
In this paper,we are concerned with the existence and non-existence of global solutions of a semi-linear heat equation with fractional Laplacian.We obtain some extension of results of Weissler who considered the case ...In this paper,we are concerned with the existence and non-existence of global solutions of a semi-linear heat equation with fractional Laplacian.We obtain some extension of results of Weissler who considered the case α = 1,and h ≡ 1.展开更多
We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove ...We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma.展开更多
We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We ...We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We also prove the non-existence of radially symmetric solutions to the singular elliptic equation in , as where .展开更多
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ...This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.展开更多
文摘This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.
基金supported by the Beijing Natural Science Foundation(1212003)。
文摘Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.
基金supported by the National Natural Science Foundation of China (11961060)the Graduate Research Support of Northwest Normal University (2021KYZZ01032)。
文摘In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.
文摘The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J.E.Dunn and J.Serrin(1985),in the case of van der Waals gas.Under the small initial perturbation,the proof of the global existence is based on an elementary energy method using the continuation argument of local solution.Moreover,the uniqueness of global solutions and large time behavior of the density are given.It is one of the main difficulties that the pressure p is not the increasing function of the densityρ.
基金This work was supported by the National Natural Science Foundation of China(Grant No.52174057)the Science and Technology Project of Changzhou City(Grant No.CJ20210136)+1 种基金the General Project of Natural Science Research in Jiangsu Universities(Grant No.20KJB440004)the Science and technology program of Changzhou University(Grant No.ZMF22020068).
文摘Asphaltenes are the most elusive substances in waxy crude oil,especially the complex structures,which leads to significant precipitation and aggregation characteristics of asphaltenes,and affects the asphaltenes-wax interaction.In this study,the concept of the existence state of asphaltenes was introduced to semi-quantitatively investigate the precipitation and aggregation characteristics of asphaltenes.On this basis,the influence of the existence state of asphaltenes on wax deposition was studied by coldfinger device and high-temperature gas chromatography,and the composition and properties of the deposits were analyzed.Four main findings were made:(1)As the asphaltene concentration increases,the existence state of asphaltenes gradually transitions from dispersed state to aggregated state,and the asphaltene concentration of 0.30 wt%in this study is the starting point of the transition.(2)The existence state of asphaltenes in crude oil does affect the process of wax deposition,as shown in the fact that the dispersed asphaltenes promote the occurrence of wax deposition,while the aggregated asphaltenes can inhibit wax deposition.(3)In the presence of the aggregated asphaltenes,that is,when the asphaltene concentration is higher than 0.30 wt%,the shedding phenomenon of deposit layer was observed,and with the increase of aggregated asphaltenes,the deposit layer fell off earlier.(4)With the increase of the dispersed asphaltenes,the wax appearance temperature(WAT)and wax content of the deposits all showed an increasing trend,while with the appearance of the aggregated asphaltenes,the above situation was reversed.The findings of this study can help for better understanding of the interaction between the asphaltenes and wax in wax deposition.
基金Supported by the National Natural Science Foundation of China(11961060)Graduate Research Support of Northwest Normal University(2021KYZZ01032)。
文摘In this paper,we focus on a general n-dimension system of k-Hessian equations.By introducing some new suitable growth conditions,the existence results of radial k-admissible solutions of the k-Hessian system are obtained.Our approach is largely based on the well-known fixed-point theorem.
基金supported by the Natural Science Foundation of China(11771166,12071169)the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。
文摘In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.
文摘This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).
文摘The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.
文摘In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.
文摘Any journalist would consider it a career highlight to cover a major historical event or witness a ground-breaking breakthrough.I am thankful that the milestone 20th National Congress of the Communist Party of China (CPC) came as a fortuitous stroke of serendipity in my professional life.
基金Supported by National Natural Science Foundation of China(41771565).
文摘[Objectives]To explore the evolution of the legal system of farmland protection and explore the rules and characteristics of policy development based on the theory and logic of institutional change since China's reform and opening up,reveal the problems and deep-seated reasons of its legislation,clarify the direction of farmland protection in the new period,and solve the"non-agricultural""non-grain"and ecological problems of farmland.[Methods]Literature analysis and inductive deduction methods were used.[Results]The evolution of the farmland protection legal system has gone through the process of"national consciousness-policy guidelines-institutional system",the change from"single subject to multiple subjects";change from the use of"one-way administrative means to coordinated use of administrative,economic and technical means".The practical problems of the farmland protection legal system are mainly due to the insufficient systematization of the farmland protection legal system itself,the generalization of quantity protection,the transformation of quality protection,and the absence of ecological protection.[Conclusions]It is recommended to improve the existing farmland protection legal system from the establishment of the Farmland Protection Law,the improvement of the farmland protection public participation mechanism and supervision mechanism,the establishment of the farmland quality construction and improvement system,the differentiated farmland occupation and supplementation balance system,and the ecological restoration system.
文摘托马斯.阿奎那的形而上学是以是(being)为中心、以本质(essence)和存在(existence)的关系学说为枢纽的存在论。阿奎那认为,形而上学或存在论所探讨的特殊的固有对象即是是(to on,esse,being)自身,或者称之为是之所以为是(esse in quantum esse,being as beinginjeneral)。他在论证是自身时强调实在意义上的是重于逻辑意义的是。是(being)包括本质(essence)与存在(existence);本质(essence)与存在(existence)皆为是者(beings)。而存在(existence)先于本质(essence);存在(existence)是是(being)之最具体的、个别的、实体的、独一无二的完美实现(act)。托马斯.阿奎那的存在论哲学颠覆了传统哲学中存在与本质的位置,它以一种存在主义代替本质主义,从而在形而上学历史上掀起一场革命。
文摘China English is an objective existence as a performance variety used in China.It is based on standard English and possesses Chinese characteristics.The Chinese characteristics of China English are reflected in the phonology,vocabulary,syntax,rhetoric and text,particularly in the vocabulary.This essay will discuss the features of China English from the following three aspects: the development of English in China;the comparison between China English,Pidgin English and Chinese English and the Chinese words borrowed by English.
基金supported by National Natural Science Foundation of China(10976026)
文摘In this paper,we are concerned with the existence and non-existence of global solutions of a semi-linear heat equation with fractional Laplacian.We obtain some extension of results of Weissler who considered the case α = 1,and h ≡ 1.
文摘We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma.
文摘We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We also prove the non-existence of radially symmetric solutions to the singular elliptic equation in , as where .
基金The research supported by the National Natural Science Foundation of China.
文摘This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.
