In this article, we study a class of nonlinear elliptic systems in regular domains of with compact boundary. More precisely, we prove the existence of bounded positive continuous solutions to the system , , subject to some Dirichlet conditions. Our approach is essentially based on properties of functions in a Kato class 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
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