1. Introduction Let Ω be a smooth bounded domain in R~n with n≥2. We are concerned with the eigenvalue problem where v is the unit outward normal to Ω. According to the theory of eigenvalue, problem (1.1) has discr...1. Introduction Let Ω be a smooth bounded domain in R~n with n≥2. We are concerned with the eigenvalue problem where v is the unit outward normal to Ω. According to the theory of eigenvalue, problem (1.1) has discrete real eigenvalue. They can be lined into展开更多
This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coeffici...This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrated some special dynamical behaviors of the positive solutions of this system which the persistence of the coexistence of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable.展开更多
This paper is concerned with the existence of nontrivial solutions of the somilinear olliptio equations on unbounded domain Ω in R~n, N≥2. These results extend Rose of [11], [13] and [16]. The main tool is variation...This paper is concerned with the existence of nontrivial solutions of the somilinear olliptio equations on unbounded domain Ω in R~n, N≥2. These results extend Rose of [11], [13] and [16]. The main tool is variational methods in this paper.展开更多
文摘1. Introduction Let Ω be a smooth bounded domain in R~n with n≥2. We are concerned with the eigenvalue problem where v is the unit outward normal to Ω. According to the theory of eigenvalue, problem (1.1) has discrete real eigenvalue. They can be lined into
基金supported by the National Natural Science Foundation of China(11271120,11426099)the Project of Hunan Natural Science Foundation of China(13JJ3085)
文摘This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrated some special dynamical behaviors of the positive solutions of this system which the persistence of the coexistence of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable.
文摘This paper is concerned with the existence of nontrivial solutions of the somilinear olliptio equations on unbounded domain Ω in R~n, N≥2. These results extend Rose of [11], [13] and [16]. The main tool is variational methods in this paper.
