Infinitely many solutions for operator equations involving duality mappings on Orlicz-Sobolev spaces
Keywords
Critical points, fountain theorem, dual fountain theorem, duality mappings, Orlicz-Sobolev spacesAbstract
Let $X$ be a real reflexive and separable Banach space having the Kadeč-Klee property, compactly imbedded in the real Banach space $V$ and let $G\colon V\rightarrow {\mathbb R} $ be a differentiable functional. By using ``fountain theorem'' and ``dual fountain theorem'' (Bartsch [< i> Infinitely many solutions of a symmetric Dirichlet problem< /i> , Nonlinear Anal. < b> 20< /b> (1993), 1205–1216] and Bartsch-Willem [< i> On an elliptic equation with concave and convex nonlinearities< /i> , Proc. Amer. Math. Soc. < b> 123< /b> (1995), 3555–3561], respectively), we will study the multiplicity of solutions for operator equation $$ J_{\varphi}u=G^{\prime}(u), $$ 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.Downloads
Published
2009-09-01
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1.
DINCA, George and MATEI, Pavel. Infinitely many solutions for operator equations involving duality mappings on Orlicz-Sobolev spaces. Topological Methods in Nonlinear Analysis. Online. 1 September 2009. Vol. 36, no. 1, pp. 49 - 76. [Accessed 29 March 2024].
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