Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media. (12th June 2005)

• Record Type: Journal Article
• Authors: Motreanu, Dumitru; RăDulescu, Vicenţiu
• Is Part Of: Boundary value problems. Volume 2(2005)
• Page Start: 107
• Page End: 127
• Publication Date: 2005-06-12
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/BVP.2005.107
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We study nonlinear eigenvalue problems of the type− div ( a ( x ) ∇ u ) = g ( λ, x, u ) inℝ N, wherea ( 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.