Existence of positive bounded solutions for nonlinear elliptic systems

Electronic Journal of Differential Equations

关键词: Green function;    Kato class;    nonlinear elliptic systems;    positive solution;    Schauder fixed point theorem;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this article, we study a class of nonlinear elliptic systemsin regular domains of $mathbb{R}^n(ngeq 3)$ with compact boundary.More precisely, we prove the existence of bounded positive continuoussolutions to the system $Delta u=lambda f(.,u,v)$,$Delta v=mu g(.,u,v)$, subject to some Dirichlet conditions.Our approach is essentially based on properties of functions ina Kato class $K^{infty }(D)$ and the Schauder fixed point theorem.

【 授权许可】

Unknown