This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of...This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.展开更多
In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other...In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other predators consume prey according to the Beddington-DeAngelis functional response, based on the coincidence degree theory, the existence of positive periodic solutions of nonautonomous predator-prey system with impulses and periodic delays is obtained under suitable conditions.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
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
A two-species predator-prey system with time delay in a two-patch environment is investigated. By using a continuation theorem based on coincidence degree theory, we obtain some sufficient conditions for the existence...A two-species predator-prey system with time delay in a two-patch environment is investigated. By using a continuation theorem based on coincidence degree theory, we obtain some sufficient conditions for the existence of periodic solution for the system.展开更多
In this paper, a nonautonomous periodic model of population with time delays and impulses, which arises in order to describe the control of a single population of cells, is studied. By the coincidence degree theory we...In this paper, a nonautonomous periodic model of population with time delays and impulses, which arises in order to describe the control of a single population of cells, is studied. By the coincidence degree theory we obtain the conditions for the existence of periodic solution of this system.展开更多
In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions u...In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.展开更多
In this paper,we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Kras- noselskii fixed point theorem for cone map and the Leg...In this paper,we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Kras- noselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.展开更多
In this paper，we consider the Kolmogorov type n-species competition systems with forced terms．We prove that this system is permanent in the case of which there are positive forced terms in this system;and if there a...In this paper，we consider the Kolmogorov type n-species competition systems with forced terms．We prove that this system is permanent in the case of which there are positive forced terms in this system;and if there are several negative forced terms in this system，it has at least two positive periodic solutions.展开更多
In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the f...In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.展开更多
Existence and nonexistence criteria are established for the positive periodic solutions of two species population growth with periodic delay by applying continuation theorem of coincidence degree theory.
By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)...By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x 1(t)(b 1(t)-a 11 (t)x 1(t)-a 12 (t)x 2(t)-a 13 (t)x 3(t))+S 1(t) x 2′(t)=x 2(t)(-b 2(t)+a 21 (t)x 1(t)-a 22 (t)x 2(t)-a 23 (t)x 3(t))+S 2(t) x 3′(t)=x 3(t)(-b 3(t)+a 31 (t)x 1(t)-a 32 (t)x 2(t)-a 33 (t)x 3(t))+S 3(t)where b i(t),a ij (t)(i,j=1,2,3) are positive continuous T \|periodic functions, S i(t)(i=1,2,3) are nonnegative continuous T \|periodic functions.展开更多
Based on the classic Lotlk-Volterra cooperation model, we establish a time-delay model of which a species cannot survive independently. By continuation theorem, we discuss existence of positive periodic solutions of t...Based on the classic Lotlk-Volterra cooperation model, we establish a time-delay model of which a species cannot survive independently. By continuation theorem, we discuss existence of positive periodic solutions of the model.展开更多
The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-...The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-periodic solutions under certain growth conditions imposed on f.Applications will be presented to illustrate the main results.展开更多
A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response,diffusion,and time delays is investigated. The model consists of n competing preys and one predator,and the predator and one...A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response,diffusion,and time delays is investigated. The model consists of n competing preys and one predator,and the predator and one prey are confined to one patch. First,concepts and results concerning the continuation theorem of coincidence degree are summarized. Then,a system of algebraic equations is proved to have a unique solution. Finally,the sufficient conditions for the existence of a difference system are established. The result is substantiated through numerical simulation.展开更多
In the present paper,we consider the existence of positive periodic solu-tions for a kind of delay Logistic equations.By using a fixed point theorem in cones,we give some new existence results of single and multiple p...In the present paper,we consider the existence of positive periodic solu-tions for a kind of delay Logistic equations.By using a fixed point theorem in cones,we give some new existence results of single and multiple positive periodic solutionsfor a kind of delay Logistic equations.Some biomathematical models are presentedto illustrate our results.展开更多
基金Supported by the Natural Science Foundation of Hunan Province（12JJ6006） Supported by the Science Foundation of Department of Science and Technology of Hunan Province（2012FJ3107）
文摘This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.
文摘In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other predators consume prey according to the Beddington-DeAngelis functional response, based on the coincidence degree theory, the existence of positive periodic solutions of nonautonomous predator-prey system with impulses and periodic delays is obtained under suitable conditions.
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.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
文摘A two-species predator-prey system with time delay in a two-patch environment is investigated. By using a continuation theorem based on coincidence degree theory, we obtain some sufficient conditions for the existence of periodic solution for the system.
文摘In this paper, a nonautonomous periodic model of population with time delays and impulses, which arises in order to describe the control of a single population of cells, is studied. By the coincidence degree theory we obtain the conditions for the existence of periodic solution of this system.
基金Supported by the National Natural Sciences Foundation of China(10361006)Supported by the Natural Sciences Foundation of Yunnan Province(2003A0001M)Supported by the Jiangsu "Qing-lanProject" for Excellent Young Teachers in University(2006)
基金The work was supported by science fundation for young teachers of Northeast Normal University (20060108).
文摘In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.
文摘In this paper,we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Kras- noselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.
文摘In this paper，we consider the Kolmogorov type n-species competition systems with forced terms．We prove that this system is permanent in the case of which there are positive forced terms in this system;and if there are several negative forced terms in this system，it has at least two positive periodic solutions.
基金Project(10471153) supported by the National Natural Science Foundation of China project supported by the Natural Science Foundation of Central South University
文摘In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.
文摘Existence and nonexistence criteria are established for the positive periodic solutions of two species population growth with periodic delay by applying continuation theorem of coincidence degree theory.
文摘By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x 1(t)(b 1(t)-a 11 (t)x 1(t)-a 12 (t)x 2(t)-a 13 (t)x 3(t))+S 1(t) x 2′(t)=x 2(t)(-b 2(t)+a 21 (t)x 1(t)-a 22 (t)x 2(t)-a 23 (t)x 3(t))+S 2(t) x 3′(t)=x 3(t)(-b 3(t)+a 31 (t)x 1(t)-a 32 (t)x 2(t)-a 33 (t)x 3(t))+S 3(t)where b i(t),a ij (t)(i,j=1,2,3) are positive continuous T \|periodic functions, S i(t)(i=1,2,3) are nonnegative continuous T \|periodic functions.
文摘Based on the classic Lotlk-Volterra cooperation model, we establish a time-delay model of which a species cannot survive independently. By continuation theorem, we discuss existence of positive periodic solutions of the model.
基金The first author was supported by the Science Foundation of Educational Committee of HunanProvince ( 99C0 1 ) and the second author by the National Natural Science Foundation of China ( 1 9871 0 0 5 )
文摘The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-periodic solutions under certain growth conditions imposed on f.Applications will be presented to illustrate the main results.
基金The National Natural Science Foundation of China (Nos.60671063,10571113,and 10871122)
文摘A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response,diffusion,and time delays is investigated. The model consists of n competing preys and one predator,and the predator and one prey are confined to one patch. First,concepts and results concerning the continuation theorem of coincidence degree are summarized. Then,a system of algebraic equations is proved to have a unique solution. Finally,the sufficient conditions for the existence of a difference system are established. The result is substantiated through numerical simulation.
文摘In the present paper,we consider the existence of positive periodic solu-tions for a kind of delay Logistic equations.By using a fixed point theorem in cones,we give some new existence results of single and multiple positive periodic solutionsfor a kind of delay Logistic equations.Some biomathematical models are presentedto illustrate our results.
