International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 8, Pages 479-490
doi:10.1155/S0161171202010293
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 Abdelaziz Ahammou. 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.
Abstract
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.