## Differential and Integral Equations

### Multiple solutions for operator equations involving duality mappings on Orlicz-Sobolev spaces

#### Abstract

Let $X$ be a real reflexive, smooth and separable Banach space having the Kadeč-Klee property and compactly imbedded in the real Banach space $Y$ and let $G:Y\rightarrow \mathbb{R}$ be a differentiable functional. By using the "fountain theorem" (Bartsch [3]), we will study the multiplicity of solutions for the operator equation $J_{\varphi}u=G^{\prime}(u)\text{,}$ where $J_{\varphi}$ is the duality mapping on $X$, corresponding to the gauge function $\varphi$. Equations having the above form with $J_{\varphi}$ a duality mapping on Orlicz-Sobolev spaces are considered as applications. As particular cases of the latter results, some multiplicity results concerning duality mappings on Sobolev spaces are derived.

#### Article information

Source
Differential Integral Equations, Volume 21, Number 9-10 (2008), 891-916.

Dates
First available in Project Euclid: 20 December 2012