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Article: Existence of multiple positive solutions of quasilinear elliptic problems in [R.sup.N].

Article from:
Advances in Dynamical Systems and Applications
Article date:
June 1, 2007
Author:
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Abstract

This paper concerns quasilinear elliptic equations of the form

-div ([[absolute value of [nabla]u].sup.p-2] [nabla]u) = [lambda]a (x)u(x) [[absolute value of u].sup.p-2] (1 - [[absolute value of u].sup.[gamma]]

in [R.sup.N] with p > 1 and a(x) changes sign. We discuss the question of existence and multiplicity of solutions when a(x) has some specific properties.

AMS subject classification: 35J70, 35B32, 35B40.

Keywords: The p-Laplacian, variational method, multiple solutions.

1. Introduction

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