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International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 8, Pages 479-490

On the existence of bounded solutions of nonlinear elliptic systems

Département des Mathématiques et Informatique, Faculté des Sciences, Université Chouaib Doukkali, BP 20, El Jadida 24000, Morocco

Received 24 March 2000; Revised 13 August 2000

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the existence of bounded solutions to the elliptic system Δpu=f(u,v)+h1 in Ω, Δqv=g(u,v)+h2 in Ω, u=v=0 on Ω, non-necessarily potential systems. The method used is a shooting technique. We are concerned with the existence of a negative subsolution and a nonnegative supersolution in the sense of Hernandez; then we construct some compact operator T and some invariant set K where we can use the Leray Schauder's theorem.