We study the existence and the regularity of solutions for a class of nonlocal equations involving the fractional Laplacian operator with singular nonlinearity and Radon measure data.
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, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of...In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of solving by iterative method.展开更多
In this paper, we derive a simple and efficient matrix formulation using Laguerre polynomials to solve the singular integral equation with degenerate kernel. This method is based on replacement of the unknown function...In this paper, we derive a simple and efficient matrix formulation using Laguerre polynomials to solve the singular integral equation with degenerate kernel. This method is based on replacement of the unknown function by truncated series of well known Laguerre expansion of functions. This leads to a system of algebraic equations with Laguerre coefficients. Thus, by solving the matrix equation, the coefficients are obtained. Some numerical examples are included to demonstrate the validity and applicability of the proposed method.展开更多
A class of quasi-linear singularly perturbed boundary value problems with singular equation is considered. Under suitable conditions, the existence and asymptotic behavior of a solution for the boundary value problem ...A class of quasi-linear singularly perturbed boundary value problems with singular equation is considered. Under suitable conditions, the existence and asymptotic behavior of a solution for the boundary value problem are studied by using the theory of differential inequalities,and the uniformly valid asymptotic expansion of solution with boundary layer is obtained.展开更多
In this paper,the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point t...In this paper,the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.展开更多
In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coeffici...In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}.展开更多
Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.
By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs,direct solutions of some singular integral equations with variable coefficients are discussed an...By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs,direct solutions of some singular integral equations with variable coefficients are discussed and the explicit formulas for these solutions are obtained.展开更多
In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is t...In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L2[-π, π].展开更多
This paper deals with the degenerate and singular parabolic equations coupled via nonlinear nonlocal reactions, subject to zero-Dirichlet boundary conditions. After giving the existence and uniqueness of local classic...This paper deals with the degenerate and singular parabolic equations coupled via nonlinear nonlocal reactions, subject to zero-Dirichlet boundary conditions. After giving the existence and uniqueness of local classical nonnegative solutions, we show critical blowup exponents for the solutions of the system. Moreover, uniform blow-up behaviors near the blow-up time are obtained for simultaneous blow-up solutions, divided into four subcases.展开更多
In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM...In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.展开更多
In this paper using the method of 'The Two-Variable Expansion Procedure' we again discuss the construction of asymptotic expression of solution of general boundary value problem for higher order ellitptic equa...In this paper using the method of 'The Two-Variable Expansion Procedure' we again discuss the construction of asymptotic expression of solution of general boundary value problem for higher order ellitptic equation containing two-parameter whose boundary condition is more general than (1)We give asymptotic expression of solution as well as the estimation corresponding to the remainder term.展开更多
This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an...This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of.展开更多
The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study a...The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.展开更多
This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and ...This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.展开更多
We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional derivatives.The main ingredient of the proposed method is to recast the p...We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional derivatives.The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations.Then,a Legendre-based spectral collocation method is developed for solving the transformed system.Therefore,we can make good use of the advantages of the Gauss quadrature rule.We present the construction and analysis of the collocation method.These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange equations.Two numerical examples are given to confirm the convergence analysis and robustness of the scheme.展开更多
This paper proposes the combined Laplace-Adomian decomposition method (LADM) for solution two dimensional linear mixed integral equations of type Volterra-Fredholm with Hilbert kernel. Comparison of the obtained resul...This paper proposes the combined Laplace-Adomian decomposition method (LADM) for solution two dimensional linear mixed integral equations of type Volterra-Fredholm with Hilbert kernel. Comparison of the obtained results with those obtained by the Toeplitz matrix method (TMM) demonstrates that the proposed technique is powerful and simple.展开更多
To improve the thermoelectric converting performance in applications such as power generation,reutilization of heat energy,refrigeration,and ultrasensitive sensors in scramjet engines,a thermoelectric film/substrate s...To improve the thermoelectric converting performance in applications such as power generation,reutilization of heat energy,refrigeration,and ultrasensitive sensors in scramjet engines,a thermoelectric film/substrate system is widely designed and applied,whose interfacial behavior dominates the strength and service life of thermoelectric devices.Herein,a theoretical model of a thermoelectric film bonded to a graded substrate is proposed.The interfacial shear stress,the normal stress in the thermoelectric film,and the stress intensity factors affected by various material and geometric parameters are comprehensively studied.It is found that adjusting the inhomogeneity parameter of the graded substrate,thermal conductivity,and current density of the thermoelectric film can reduce the risk of interfacial failure of the thermoelectric film/graded substrate system.Selecting a stiffer and thicker thermoelectric film is advantageous to the reliability of the thermoelectric film/graded substrate system.The results should be of great guiding significance for the present and upcoming applications of thermoelectric materials in various fields.展开更多
文摘We study the existence and the regularity of solutions for a class of nonlocal equations involving the fractional Laplacian operator with singular nonlinearity and Radon measure 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.
文摘In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of solving by iterative method.
文摘In this paper, we derive a simple and efficient matrix formulation using Laguerre polynomials to solve the singular integral equation with degenerate kernel. This method is based on replacement of the unknown function by truncated series of well known Laguerre expansion of functions. This leads to a system of algebraic equations with Laguerre coefficients. Thus, by solving the matrix equation, the coefficients are obtained. Some numerical examples are included to demonstrate the validity and applicability of the proposed method.
基金Supported by the National Natural Science Foundation of China (40876010)the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences (KZCX2-YW-Q03-08)the R & D Special Fund for Public Welfare Industry (meteorology) (GYHY200806010)
文摘A class of quasi-linear singularly perturbed boundary value problems with singular equation is considered. Under suitable conditions, the existence and asymptotic behavior of a solution for the boundary value problem are studied by using the theory of differential inequalities,and the uniformly valid asymptotic expansion of solution with boundary layer is obtained.
基金supported by the National Nature Science Foundation of China (10671167)
文摘In this paper,the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}.
基金Supported by the Natural Science Foundation of Guangdong Province (S2011010001900)the Guangdong Higher Education Foundation for High-Level Talents
文摘Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.
基金Supported by the NNSF of china(11171298)SuppoSed by the Natural Science Foundation of Zhejiang Province(Y6110425,Y604563)
文摘By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs,direct solutions of some singular integral equations with variable coefficients are discussed and the explicit formulas for these solutions are obtained.
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L2[-π, π].
基金Supported by the National Natural Science Foundation of China（11201483） Supported by the Natural Science Foundation of Shandong Province Supported by the Fundamental Research Funds for the Central Universities
文摘This paper deals with the degenerate and singular parabolic equations coupled via nonlinear nonlocal reactions, subject to zero-Dirichlet boundary conditions. After giving the existence and uniqueness of local classical nonnegative solutions, we show critical blowup exponents for the solutions of the system. Moreover, uniform blow-up behaviors near the blow-up time are obtained for simultaneous blow-up solutions, divided into four subcases.
文摘In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.
文摘In this paper using the method of 'The Two-Variable Expansion Procedure' we again discuss the construction of asymptotic expression of solution of general boundary value problem for higher order ellitptic equation containing two-parameter whose boundary condition is more general than (1)We give asymptotic expression of solution as well as the estimation corresponding to the remainder term.
文摘This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of.
文摘The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.
基金Project supported by the National Natural Science Foundation of China(Nos.12072209,U21A2043012192211)+1 种基金the Natural Science Foundation of Hebei Province of China(No.A2020210009)the S&T Program of Hebei Province of China(No.225676162GH)。
文摘This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.
基金The Russian Foundation for Basic Research(RFBR)Grant No.19-01-00019.
文摘We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional derivatives.The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations.Then,a Legendre-based spectral collocation method is developed for solving the transformed system.Therefore,we can make good use of the advantages of the Gauss quadrature rule.We present the construction and analysis of the collocation method.These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange equations.Two numerical examples are given to confirm the convergence analysis and robustness of the scheme.
文摘This paper proposes the combined Laplace-Adomian decomposition method (LADM) for solution two dimensional linear mixed integral equations of type Volterra-Fredholm with Hilbert kernel. Comparison of the obtained results with those obtained by the Toeplitz matrix method (TMM) demonstrates that the proposed technique is powerful and simple.
基金Project supported by the National Natural Science Foundation of China(Nos.11972363 and12272401)the Opening Project of State Key Laboratory of Solid Lubrication(Lanzhou Institute of Chemical Physics)(No.LSL-20012001)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-E-0221G01)。
文摘To improve the thermoelectric converting performance in applications such as power generation,reutilization of heat energy,refrigeration,and ultrasensitive sensors in scramjet engines,a thermoelectric film/substrate system is widely designed and applied,whose interfacial behavior dominates the strength and service life of thermoelectric devices.Herein,a theoretical model of a thermoelectric film bonded to a graded substrate is proposed.The interfacial shear stress,the normal stress in the thermoelectric film,and the stress intensity factors affected by various material and geometric parameters are comprehensively studied.It is found that adjusting the inhomogeneity parameter of the graded substrate,thermal conductivity,and current density of the thermoelectric film can reduce the risk of interfacial failure of the thermoelectric film/graded substrate system.Selecting a stiffer and thicker thermoelectric film is advantageous to the reliability of the thermoelectric film/graded substrate system.The results should be of great guiding significance for the present and upcoming applications of thermoelectric materials in various fields.
