Qualitative properties of a cooperative degenerate Lotka-Volterra model

Advances in Difference Equations

Jiebao Sun¹  Dazhi Zhang¹  Boying Wu¹ 

[1] Department of Mathematics, Harbin Institute of Technology, Harbin, China

关键词: Periodic Solution;    Weak Solution;    Initial Boundary;    Comparison Principle;    Parabolic System;   

DOI  :  10.1186/1687-1847-2013-281

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper considers a kind of degenerate parabolic systems. First, we consider the initial boundary value problem of the two-species degenerate parabolic cooperative system. By using the method of a parabolic regularization and energy estimate, we establish the existence of the weak solution of the problem. Then we establish the comparison principle and discuss the uniqueness and the uniform bound. At last, we consider the periodic boundary value problem of the system. By constructing a pair of ordered upper and lower solutions, we establish the existence of nontrivial nonnegative periodic solutions.

【 授权许可】

CC BY