Báo Cáo Báo cáo khoa học Existence and multiplicity of weak solutions for a class of degenerate nonlinear el

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 the a Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The goal of this paper is to study a nonlinear elliptic equation in which the divergence form operator ư div(a(x, ∇u)) is involved. Such operators appear in many nonlinear diffusion