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
In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential eq...In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.展开更多
In this paper, a three species difFusive predator-prey modei with functional response and periodic stocking is studied, where all parameters are time depen-dent. By using new theorem of coincidence degree theory, the ...In this paper, a three species difFusive predator-prey modei with functional response and periodic stocking is studied, where all parameters are time depen-dent. By using new theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.展开更多
In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results ...In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.展开更多
This paper is concerned with the existence of positive periodic solutions to a second order functional differential equation with infinite delay.Under the appropriate conditions,some existence and multiplicity of posi...This paper is concerned with the existence of positive periodic solutions to a second order functional differential equation with infinite delay.Under the appropriate conditions,some existence and multiplicity of positive periodic solutions are derived by an abstract fixed-point theorem.展开更多
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.
基金Supported by National Natural Science Foundation of China (10971229)Doctoral Foundation of Guilin University of Technology (2010)National Research Program of China(2007CB714107)
基金The paper is supported by Youth Funds of JXUFE,JXJG07436.
文摘In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.
基金Research supported by National Natural Science Foundation of China(No.19531070)the Youth Project Foundation of Hubei Province Education Department(No.2002B00002)
文摘In this paper, a three species difFusive predator-prey modei with functional response and periodic stocking is studied, where all parameters are time depen-dent. By using new theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.
基金Supported by the Natural Science Foundation of Anhui Province(2004KJ028).
文摘In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.
基金Supported by the Natural Science Foundation of Anhui Province Education Department (KJ2009A49)the Natural Science Foundation of Bengbu College (2010ZR04)
文摘This paper is concerned with the existence of positive periodic solutions to a second order functional differential equation with infinite delay.Under the appropriate conditions,some existence and multiplicity of positive periodic solutions are derived by an abstract fixed-point theorem.
