Abstract and Applied Analysis
Volume 2005 (2005), Issue 2, Pages 95-104

On a class of semilinear elliptic equations with boundary conditions and potentials which change sign

M. Ouanan and A. Touzani

Department of Mathematics and Informatics, Faculty of Sciences Dhar-Mahraz, P.O. Box 1796 Atlas-Fez, Fez, Morocco

Received 19 May 2004

Copyright © 2005 M. Ouanan and A. Touzani. 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 nontrivial solutions for the problem Δu=u, in a bounded smooth domain Ω, with a semilinear boundary condition given by u/ν=λuW(x)g(u), on the boundary of the domain, where W is a potential changing sign, g has a superlinear growth condition, and the parameter λ]0,λ1];λ1 is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.