A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one pred...One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.展开更多
In this paper, a system of reaction-diffusion equations arising in ecoepidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded re...In this paper, a system of reaction-diffusion equations arising in ecoepidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. Local stability of the constant positive solution is considered. A number of existence and non-existence results about the nonconstant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the prey with disease is treated as a bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steadystate solution under some conditions.展开更多
In this paper, we mainly study a diffusive Lotka-Volterra competition-advection system with lethal boundary conditions in a general heterogeneous environment. By using the basic theory of partial differential equation...In this paper, we mainly study a diffusive Lotka-Volterra competition-advection system with lethal boundary conditions in a general heterogeneous environment. By using the basic theory of partial differential equations and some nonlinear analysis techniques, we investigate the existence, uniqueness and global asymptotic behavior of steady-state solutions of the system equations. The existence, uniqueness and global asymptotic behavior of steady-state solutions are proved by upper and lower solutions, maximum principle and other methods. In theory, the methods and skills to deal with this kind of nonlinear problem are further developed, which provides a theoretical basis for understanding some practical problems.展开更多
In this paper,a system of reaction-diffusion equations arising in a nutrient-phytoplankton populations is investigated.The equations model a situation in which phytoplankton population is divided into two groups,namel...In this paper,a system of reaction-diffusion equations arising in a nutrient-phytoplankton populations is investigated.The equations model a situation in which phytoplankton population is divided into two groups,namely susceptible phytoplankton and infected phytoplankton.A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given.If the diffusion coefficient of the infected phytoplankton is treated as bifurcation parameter,non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.展开更多
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
基金This work is supported by National Science Foundation of China and the Fundes of Institute of Math (opened) Academic Sinica.
文摘One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.
基金The NSF (10771085) of Chinathe Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Educationthe 985 program of Jilin University
文摘In this paper, a system of reaction-diffusion equations arising in ecoepidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. Local stability of the constant positive solution is considered. A number of existence and non-existence results about the nonconstant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the prey with disease is treated as a bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steadystate solution under some conditions.
文摘In this paper, we mainly study a diffusive Lotka-Volterra competition-advection system with lethal boundary conditions in a general heterogeneous environment. By using the basic theory of partial differential equations and some nonlinear analysis techniques, we investigate the existence, uniqueness and global asymptotic behavior of steady-state solutions of the system equations. The existence, uniqueness and global asymptotic behavior of steady-state solutions are proved by upper and lower solutions, maximum principle and other methods. In theory, the methods and skills to deal with this kind of nonlinear problem are further developed, which provides a theoretical basis for understanding some practical problems.
基金Supported by the National Natural Science Foundation of China(No.10771085)
文摘In this paper,a system of reaction-diffusion equations arising in a nutrient-phytoplankton populations is investigated.The equations model a situation in which phytoplankton population is divided into two groups,namely susceptible phytoplankton and infected phytoplankton.A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given.If the diffusion coefficient of the infected phytoplankton is treated as bifurcation parameter,non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.
