EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF DEGENERATE NONLINEAR ELLIPTIC

EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF DEGENERATE NONLINEAR ELLIPTIC EQUATIONS ˘ MIHAI MIHAILESCU Received 11 January 2005; Revised 4 July 2005; Accepted 17 July 2005 The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN . The solutions will be obtained in a subspace of the Sobolev space W 1,p (RN ). The proofs rely essentially on the Mountain Pass theorem and on Ekeland’s Variational principle. Copyright © 2006 Mihai Mih˘ ilescu. This is an open access article distributed under...