Existence of positive bounded solutions for nonlinear elliptic systems

Abstract

In this article, we study a class of nonlinear elliptic systems in regular domains of $mathbb{R}^n(ngeq 3)$ with compact boundary. More precisely, we prove the existence of bounded positive continuous solutions 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 in a Kato class $K^{infty }(D)$ and the Schauder fixed point theorem.

Keywords

• Green function
• Kato class
• nonlinear elliptic systems
• positive solution
• Schauder fixed point theorem