Existence of non-negative solutions for predator-prey elliptic systems with a sign-changing nonlinearity

Electronic Journal of Differential Equations

关键词: Elliptic system;    non-negative solution;    existence;   

DOI  :  

来源: DOAJ

【 摘 要 】

By the method of monotone iteration and Schauder fixed point theorem,we prove the existence of non-negative solutions to the system$$displaylines{-Delta u= lambda a(x) f(v)quad hbox{in }Omega,cr-Delta v= lambda b(x) g(u)quad hbox{in } Omega,cru =v=0quad hbox{on }partial Omega,}$$for $lambda$ sufficiently small, where $Omega$ is a boundeddomain in $mathbb{R}^N$ with smooth boundary $partial Omega$and $lambda$ is a positive parameter. In this work, we allowthe sign changing nature of a and b with$a(x) b(x)leq 0, forall xin ar{Omega}$.

【 授权许可】

Unknown