通讯机构：
[Luo, Zhenguo] H;Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
关键词：
A set of easily verifiable sufficient conditions are derived to guarantee the existence and the global stability of positive periodic solutions for two-species competitive systems with multiple delays and impulses;by applying some new analysis techniques. This improves and extends a series of the well-known sufficiency theorems in the literature about the problems mentioned previously. Published: 2014 First available in Project Euclid: 2 October 2014 zbMATH: 07023067 MathSciNet: MR3193546 Digital Object Identifier: 10.1155/2014/785653
期刊：
Journal of Applied Mathematics,2014年2014(Pt.3):592543:1-592543:21 ISSN：1110-757X
通讯作者：
Luo, Zhenguo
作者机构：
[Luo, Liping; Gao, Zhenghui; Zeng, Yunhui; Yang, Liu; Luo, Zhenguo] Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.;[Luo, Zhenguo] Natl Univ Def Technol, China Dept Math, Changsha 410073, Hunan, Peoples R China.
通讯机构：
[Luo, Zhenguo] H;Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
关键词：
An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated;where we assume the model of patches with a barrier only as far as the prey population is concerned;whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional;a set of easily verifiable sufficient conditions are obtained to guarantee the existence;uniqueness;and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application;we also give two examples to illustrate the feasibility of our main results. Published: 2014 First available in Project Euclid: 2 March 2015 zbMATH: 07010692 MathSciNet: MR3191132 Digital Object Identifier: 10.1155/2014/592543
摘要：
An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results.
关键词：
By using a fixed point theorem of strict-set-contraction;which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k -set contraction;we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t)=x(t)[a(t)-f(t;x(t);x(t-τ1(t;x(t)));x(t-τn(t;x(t)));x'(t-γ1(t;x(t)));x'(t-γm(t;x(t))))];t≠tk;k∈Z+;x(tk+)=x(tk-)+θk(x(tk));k∈Z+ . As applications of our results;we also give some applications to several Lotka-Volterra models and new results are obtained. Published: 2014 First available in Project Euclid: 2 March 2015 zbMATH: 07010691 MathSciNet: MR3176824 Digital Object Identifier: 10.1155/2014/592513
摘要：
By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t) = x(t)[a(t) - f(t,x(t), x(t - tau(1)(t, x(t))), ... , x(t - tau(n)(t, x(t))), x'(t - gamma(1)(t,x(t))), ... , x'(t - gamma(m)(t, x(t))))], t not equal t(k), k subset of Z(+); x(t(k)(+)) = x(t(k)(-)) + theta(k)(x(t(k))), k subset of Z(+). As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.
通讯机构：
[Luo, Zhenguo] H;Hengyang Normal Univ, Dept Math, Hengyang 421008, Hunan, Peoples R China.
关键词：
We apply the Krasnoselskii’s fixed point theorem to study the existence of multiple positive periodic solutions for a class of impulsive functional differential equations with infinite delay and two parameters. In particular;the presented criteria improve and generalize some related results in the literature. As an application;we study some special cases of systems;which have been studied extensively in the literature. Published: 2014 First available in Project Euclid: 26 March 2014 zbMATH: 07010741 MathSciNet: MR3166787 Digital Object Identifier: 10.1155/2014/751612
摘要：
We apply the Krasnoselskii's fixed point theorem to study the existence of multiple positive periodic solutions for a class of impulsive functional differential equations with infinite delay and two parameters. In particular, the presented criteria improve and generalize some related results in the literature. As an application, we study some special cases of systems, which have been studied extensively in the literature.
作者机构：
[Luo, Liping; Yang, Liu; Luo, Zhenguo] Hengyang Normal Univ, Hengyang, Peoples R China.
通讯机构：
[Yang, Liu] H;Hengyang Normal Univ, Hengyang, Peoples R China.
关键词：
Hamiltonian System;Homoclinic Orbit;Weighted Sobolev Space;Homoclinic Solution;Positive Continuous Function
摘要：
We investigate the existence of infinitely many fast homoclinic solutions for a class of second-order nonautonomous systems. Our main tools are based on the variant fountain theorem. A criterion guaranteeing that the second-order system has infinitely many fast homoclinic solutions is obtained. Recent results from the literature are generalized and significantly improved.
关键词：
We investigate a neutral multispecies logarithmic population model with feedback control and impulse. By applying the contraction mapping principle and some inequality techniques;a set of easily applicable criteria for the existence;uniqueness;and global attractivity of positive periodic solution are established. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases. We also give an example to illustrate the applicability of our results. Published: 2013 First available in Project Euclid: 26 February 2014 zbMATH: 07095312 MathSciNet: MR3108671 Digital Object Identifier: 10.1155/2013/741043
