Multiplicity of positive solutions to a p-Laplacian equation involving critical nonlinearity

Abstract

In this paper we deal with multiplicity of positive solutions to the p-Laplacian equation of the type -div( ∇u p-2∇u) = μuq-1 + up*-1, u ∈ W01,p (Ω), where Ω ⊂ ℝN is a bounded domain, N ≥ p2, 2 ≤ p ≤ q 0 such that, for each μ ∈ (0, μ*), the equation has at least catΩ(Ω) positive solutions. © 2003 Elsevier Science (USA). All rights reserved.