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2008 Multiple solutions for operator equations involving duality mappings on Orlicz-Sobolev spaces
George Dinca, Pavel Matei
Differential Integral Equations 21(9-10): 891-916 (2008).

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.

Citation

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George Dinca. Pavel Matei. "Multiple solutions for operator equations involving duality mappings on Orlicz-Sobolev spaces." Differential Integral Equations 21 (9-10) 891 - 916, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35419
MathSciNet: MR2483340

Subjects:
Primary: 35R20
Secondary: 46E30, 46E35, 47J30

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 9-10 • 2008
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