A result of multiplicity of solutions for a class of quasilinear equations

Abstract

We establish the multiplicity of positive weak solutions for the quasilinear Dirichlet problem-Lpu + |u|p-2u = h(u) in Ωλ, u = 0 on ∂Ωλ, where Ωλ = λΩ, Ω is a bounded domain in RN, λ is a positive parameter, Lpu = Δpu + Δp(u2)u and the nonlinear term h(u) has subcritical growth. We use minimax methods together with the Lyusternik-Schnirelmann category theory to get multiplicity of positive solutions. © 2012 Edinburgh Mathematical Society.