Open Access

Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media

Boundary Value Problems20052005:708605

Received: 23 September 2004

Published: 12 June 2005


We study nonlinear eigenvalue problems of the type in , where 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.

Authors’ Affiliations

Département de Mathématiques, Université de Perpignan, Perpignan, France
Department of Mathematics, University of Craiova, Craiova, Romania


© Motreanu and RăDulescu 2005