Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 107-127
doi:10.1155/BVP.2005.107

Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media

Dumitru Motreanu1 and Vicenţiu RăDulescu2

1Département de Mathématiques, Université de Perpignan, Perpignan 66860, France
2Department of Mathematics, University of Craiova, Craiova 200585, Romania

Received 23 September 2004; Revised 26 November 2004

Copyright © 2005 Dumitru Motreanu and Vicenţiu RăDulescu. 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 nonlinear eigenvalue problems of the type −div(a(x)∇u)=g(λ,x,u) in ℝN, where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality. A specific minimax method is developed without making use of Palais-Smale condition.