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
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.