期刊：
International Journal of Dynamical Systems and Differential Equations,2015年5(4):336-353 ISSN：1752-3583
通讯作者：
Zhang, Qianhong(zqianhong68@163.com)
作者机构：
[Qianhong Zhang] Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, Guizhou, China;[Jingzhong Liu] Department of Mathematics and Physics, Hunan Institute of Technology, Hengyang, Hunan, China;[Zhenguo Luo] Department of Mathematics, Hengyang Normal University, Hengyang, Hunan, China;[Yuanfu Shao] School of Science, Guilin University of Technology, Guilin, Guangxi, China
通讯机构：
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, Guizhou, China
摘要：
This paper is concerned with the existence, the boundedness and the asymptotic behaviour of the positive solutions of a second-order fuzzy nonlinear difference equations. The parameter and initial values of system are positive fuzzy numbers. Finally an example is given to illustrate the effectiveness of the results obtained.
摘要：
In this article, we are concerned with a class of fourth-order elliptic equations with sublinear perturbation and steep potential well. By using variational methods, we obtain that such equations admit at least two nontrivial solutions. We also explore the phenomenon of concentration of solutions.
摘要：
This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equations x(n+1) = A + x(n)/y(n-1)y(n-2), y(n+1) = A + y(n)/x(n-1)x(n-2), n = 0, 1,..., where A is an element of(0, infinity), x(-i) is an element of (0, infinity); y(-i) is an element of (0, infinity), i = 0, 1, 2. Some examples are given to demonstrate the effectiveness of the results obtained.
期刊：
Journal of Mathematics,2014年2014:1-13 ISSN：2314-4629
通讯作者：
Luo, Z.
作者机构：
Department of Mathematics, Hengyang Normal University, Hengyang, Hunan, 421008, China;Department of Mathematics, National University of Defense Technology, Changsha, 410073, China
通讯机构：
Department of Mathematics, Hengyang Normal University, Hengyang, Hunan, China
摘要：
By applying the fixed point theorem, we derive some new criteria for the existence of multiple positive periodic solutions for two kinds of n -dimension periodic impulsive functional differential equations with multiple delays and two parameters: x i ′ ( t ) = a i ( t ) x i ( t ) - λ b i ( t ) f i ( t , x ( t ) , x ( t - τ 1 ( t ) ) , … , x ( t - τ n ( t ) ) ) ), a.e., t > 0 , t ≠ t k , k ∈ Z + , x i ( t k + ) - x i ( t k - ) = μ c i k x i ( t k ) , i = 1,2 , … , n , k ∈ Z + , and x i ′ ( t ) = - a i ( t ) x i ( t ) + λ b i ( t ) f i ( t , x ( t ) , x ( t - τ 1 ( t ) ) , … , x ( t - τ n ( t ) ) ) ), a.e., t > 0 , t ≠ t k , k ∈ Z + , x i ( t k + ) - x i ( t k - ) = μ c i k x i ( t k ) , i = 1,2 , … , n , k ∈ Z + . As an application, we study some special cases of the previous systems, which have been studied extensively in the literature.
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
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.
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.
