Topological Methods in Nonlinear Analysis

Multiplicity results for some quasilinear elliptic problems

Abstract

In this paper, we study multiplicity of weak solutions for the following class of quasilinear elliptic problems of the form $$-\Delta_p u -\Delta u = g(u)-\lambda |u|^{q-2}u \quad \text{in } \Omega \text{ with } u=0 \text{ on } \partial\Omega,$$ where $\Omega$ is a bounded domain in ${\mathbb{R}}^n$ with smooth boundary $\partial\Omega$, $1< q< 2< p\leq n$, $\lambda$ is a real parameter, $\Delta_p u = {\rm div}(|\nabla u|^{p-2}\nabla u)$ is the $p$-Laplacian and the nonlinearity $g(u)$ has subcritical growth. The proofs of our results rely on some linking theorems and critical groups estimates.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 34, Number 1 (2009), 77-89.

Dates
First available in Project Euclid: 27 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461785685

Mathematical Reviews number (MathSciNet)
MR2581460

Zentralblatt MATH identifier
1183.35107

Citation

de Paiva, Francisco Odair; do Ó, João Marcos; de Medeiros, Everaldo Souto. Multiplicity results for some quasilinear elliptic problems. Topol. Methods Nonlinear Anal. 34 (2009), no. 1, 77--89. https://projecteuclid.org/euclid.tmna/1461785685

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