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
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 utilizing a fixed point theorem on cone, some new results on the existence ofpositive periodic solutions for nonautonomous differential equations with delay are derived.
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
By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f...By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f（n,x（n-τ1（n））,…,x（n-τm（n））,u（n-δ（n）））,△u（n）=-η（n）u（n）＋a（n）x（n-σ（n））,n∈Z.展开更多
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, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Legg...In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.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
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)=x ...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
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 ...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, eon^pts 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 solutions 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...In the present paper, we consider the existence of positive periodic solutions 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 solutions for a kind of delay Logistic equations. Some biomathematical models are presented to illustrate our results.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
We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positi...We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.展开更多
By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following n...By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation展开更多
In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u...In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u'(f)=f(t,u(t)) (t∈R), where f: R×R^+→Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.展开更多
In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of pos...In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results.展开更多
Abstract In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples ...Abstract In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples to demonstrate our results.展开更多
With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomou...With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.展开更多
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))].
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Supported by the Natural Science Foundation of Guangdong Province（032469）
文摘By utilizing a fixed point theorem on cone, some new results on the existence ofpositive periodic solutions for nonautonomous differential equations with delay are derived.
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)
文摘By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f（n,x（n-τ1（n））,…,x（n-τm（n））,u（n-δ（n）））,△u（n）=-η（n）u（n）＋a（n）x（n-σ（n））,n∈Z.
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, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.
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.
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.
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, eon^pts 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 solutions 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 solutions for a kind of delay Logistic equations. Some biomathematical models are presented to illustrate our results.
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.
文摘We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.
基金Supported by the National Natural Science Foundation of China (No.19871005).
文摘By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation
基金Project supported by the National Natural Science Foundation of China (No.10271095), the Gansu Provincial Natural Science Foundation of China (No.ZS031-A25-003-Z) and the NWNU-KJCXGC-212 Foundation
文摘In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u'(f)=f(t,u(t)) (t∈R), where f: R×R^+→Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.
基金supported by the National Natural Science Foundation of China under Grant No.11302002the Foundation of Outstanding Young Talent in University of Anhui Province of China under Grant No.2011SQRL022ZD
文摘In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results.
基金Supported by Postdoctoral Science Foundation of China (No.200114).
文摘Abstract In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples to demonstrate our results.
基金supported by the National Natural Science Foundation of China under the Grant(10426010)the Foundation of Science and Technology of Fujian Province for Young Scholars(2004J0002)+3 种基金the Foundation of Fujian Education Bureau(JA04156)the National Natural Science Foundation of China under Grant 60373067the Natural Science Foundation of Jiangsu Province,China under Grants BK2003053Qing-Lan Engineering Project of Jiangsu Province,the Foundation of Southeast University,Nanjing,China under Grant XJ030714
文摘With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.
