Infinitely many solutions for operator equations involving duality mappings on Orlicz-Sobolev spaces
Słowa kluczowe
Critical points, fountain theorem, dual fountain theorem, duality mappings, Orlicz-Sobolev spacesAbstrakt
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.Pobrania
Opublikowane
2009-09-01
Jak cytować
1.
DINCA, George & MATEI, Pavel. Infinitely many solutions for operator equations involving duality mappings on Orlicz-Sobolev spaces. Topological Methods in Nonlinear Analysis [online]. 1 wrzesień 2009, T. 36, nr 1, s. 49–76. [udostępniono 17.7.2024].
Numer
Dział
Articles
Statystyki
Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0