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Theoretical Studies on the Effects of Dispersal Corridors on the Permanence of Discrete Predator-Prey Models in Patchy Environment

We study two discrete predator-prey models in patchy environment, one without dispersal corridors and one with dispersal corridors. Dispersal corridors are passes that allow the migration of species from one patch to another and their existence may influence the permanence of the model. We will offer sufficient conditions to guarantee the permanence of the two predator-prey...

Theoretical Studies on the Effects of Dispersal Corridors on the Permanence of Discrete Predator-Prey Models in Patchy Environment

We study two discrete predator-prey models in patchy environment, one without dispersal corridors and one with dispersal corridors. Dispersal corridors are passes that allow the migration of species from one patch to another and their existence may influence the permanence of the model. We will offer sufficient conditions to guarantee the permanence of the two predator-prey...

New Results for Multipoint Singular Boundary Value Problems on a Measure Chain

We study the existence and uniqueness of positive solutions for a class of singular m-point boundary value problems of second order differential equations on a measure chain. A sharper sufficient condition for the existence and uniqueness of positive solutions as well as positive solutions is obtained by the technique of lower and upper solutions and the maximal principle theorem.

New Results for Multipoint Singular Boundary Value Problems on a Measure Chain

We study the existence and uniqueness of positive solutions for a class of singular m-point boundary value problems of second order differential equations on a measure chain. A sharper sufficient condition for the existence and uniqueness of positive solutions as well as positive solutions is obtained by the technique of lower and upper solutions and the maximal principle theorem.

Dynamical Aspects of Initial/Boundary Value Problems for Ordinary Differential Equations 2014

their support and help throughout the preparation of this special issue. Jifeng Chu Yongli Song Juntao Sun Patricia J. Y. Wong Yonghui Xia

Dynamical Aspects of Initial/Boundary Value Problems for Ordinary Differential Equations 2014

their support and help throughout the preparation of this special issue. Jifeng Chu Yongli Song Juntao Sun Patricia J. Y. Wong Yonghui Xia

Dynamical Aspects of Initial/Boundary Value Problems for Ordinary Differential Equations 2014

their support and help throughout the preparation of this special issue. Jifeng Chu Yongli Song Juntao Sun Patricia J. Y. Wong Yonghui Xia

Periodic Solutions of a Stage-Structured Plant-Hare Model with Toxin-Determined Functional Responses

The purpose of this paper is to obtain some sufficient conditions for the global existence of multiple positive periodic solutions of a delayed stage-structured plant-hare model with a toxin-determined functional response. Some novel estimation techniques to construct two open subsets for a priori bounds are employed.

Periodic Solutions of a Stage-Structured Plant-Hare Model with Toxin-Determined Functional Responses

The purpose of this paper is to obtain some sufficient conditions for the global existence of multiple positive periodic solutions of a delayed stage-structured plant-hare model with a toxin-determined functional response. Some novel estimation techniques to construct two open subsets for a priori bounds are employed.

Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems , (HS) where , , is a continuous bounded function, and the potential has a singularity at , and is the gradient of at . The novelty of this paper is that, for the case that and (HS) is nonautonomous (neither periodic nor almost periodic), we show...

Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems , (HS) where , , is a continuous bounded function, and the potential has a singularity at , and is the gradient of at . The novelty of this paper is that, for the case that and (HS) is nonautonomous (neither periodic nor almost periodic), we show...

Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy

Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies . However, this condition is very restricted. There are few functions satisfying . In some sense, this assumption is not reasonable enough. More suitable assumption should be . To the best of the authors

Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy

Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies . However, this condition is very restricted. There are few functions satisfying . In some sense, this assumption is not reasonable enough. More suitable assumption should be . To the best of the authors

Existence for Singular Periodic Problems: A Survey of Recent Results

We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.

Dynamical Aspects of Initial/Boundary Value Problems for Ordinary Differential Equations

this journal, for their support and help throughout the preparation of this special issue. Jifeng Chu Juntao Sun Patricia J. Y. Wong Yonghui Xia

Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System

This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M-predators and N-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in...

Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System

This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M-predators and N-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in...