Electron. J. Diff. Equ., Vol. 2013 (2013), No. 175, pp. 1-11.

Existence of positive bounded solutions for nonlinear elliptic systems

Faten Toumi

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.

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Faten Toumi
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: faten.toumi@fsb.rnu.tn

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