Multiplicity results for some quasilinear elliptic problems
Keywords
Quasilinear elliptic problems, p-Laplace operator, multiplicity of solutions, critical groups, linking theoremsAbstract
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 = \dive(|\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.Downloads
Published
2009-09-01
How to Cite
1.
DE PAIVA, Francisco Odair, DO Ó, João Marcos and DE MEDEIROS, Everaldo Souto. Multiplicity results for some quasilinear elliptic problems. Topological Methods in Nonlinear Analysis. Online. 1 September 2009. Vol. 36, no. 1, pp. 77 - 89. [Accessed 17 April 2024].
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