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2018 Eigenvalues of some $p(x)$-biharmonic problems under Neumann boundary conditions
Mounir Hsini, Nawal Irzi, Khaled Kefi
Rocky Mountain J. Math. 48(8): 2543-2558 (2018). DOI: 10.1216/RMJ-2018-48-8-2543

Abstract

In this paper, we study the following $p(x)$-biharmonic problem in Sobolev spaces with variable exponents \begin{equation} \begin{cases} \triangle ^{2}_{p(x)}u=\lambda ({\partial F } (x,u)/{\partial u}) & x\in \Omega , \\ {\partial u}/{\partial n}=0 & x\in \partial \Omega ,\\ {\partial }(|\triangle u|^{p(x)-2}\triangle u)/{\partial n} =a(x)|u|^{p(x)-2}u & x\in \partial \Omega . \end{cases} \end{equation} By means of the variational approach and Ekeland's principle, we establish that the above problem admits a nontrivial weak solution under appropriate conditions.

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Mounir Hsini. Nawal Irzi. Khaled Kefi. "Eigenvalues of some $p(x)$-biharmonic problems under Neumann boundary conditions." Rocky Mountain J. Math. 48 (8) 2543 - 2558, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2543

Information

Published: 2018
First available in Project Euclid: 30 December 2018

zbMATH: 06999273
MathSciNet: MR3894992
Digital Object Identifier: 10.1216/RMJ-2018-48-8-2543

Subjects:
Primary: 35D05, 35D30, 35J58, 35J60, 35J65

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 8 • 2018
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