Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 175, pp. 1-11.
Title: Existence of positive bounded solutions
for nonlinear elliptic systems
Author: Faten Toumi (Faculte des Sciences de Tunis, Tunisia)
Abstract:
In this article, we study a class of nonlinear elliptic systems
in regular domains of $\mathbb{R}^n(n\geq 3)$ 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.
Submitted August 15, 2012. Published July 29, 2013.
Math Subject Classifications: 34B15, 34B27, 35J66.
Key Words: Green function; Kato class; nonlinear elliptic systems;
positive solution; Schauder fixed point theorem.