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Dancer, E. and Guo, Z. (1994) Uniqueness and Stability for Solutions of Competing Species Equations with Large Interactions. Communications on Applied Nonlinear Analysis, 1, 19-45.

has been cited by the following article:

• TITLE: On Some Dynamics of a Diffusive Lotka-Volterra Competition-Advection System with Lethal Boundary Conditions

  AUTHORS: Dongxuan Zhao

  KEYWORDS: Global Asymptotic Stability, Competing Systems, Positive Steady-State Solution, Coexistence

  JOURNAL NAME: Applied Mathematics, Vol.12 No.4, April 19, 2021

  ABSTRACT: 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.