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2012 MULTIPLICITY RESULTS FOR A NEUMANN BOUNDARY VALUE PROBLEM INVOLVING THE $P(X)$-LAPLACIAN
F. Cammaroto, L. Vilasi
Taiwanese J. Math. 16(2): 621-634 (2012). DOI: 10.11650/twjm/1500406606

Abstract

In this paper we are interested in the multiplicity of weak solutions to the following Neumann problem involving the $p(x)$-Laplacian operator $$ \left\{ \begin{array}{ll} -\delta_{p(x)}u + \mid u \mid^{p(x)-2}u = \lambda \alpha(x) f(u) + \beta(x) g(u) \ \ \ & in \ \Omega \\ \frac{\partial u}{\partial v} = 0 \ \ \ & on \ \Omega\end{array} \right. $$ We establish the existence of at least three solutions to this problem by using, as main tool, a recent variational principle due to Ricceri.

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F. Cammaroto. L. Vilasi. "MULTIPLICITY RESULTS FOR A NEUMANN BOUNDARY VALUE PROBLEM INVOLVING THE $P(X)$-LAPLACIAN." Taiwanese J. Math. 16 (2) 621 - 634, 2012. https://doi.org/10.11650/twjm/1500406606

Information

Published: 2012
First available in Project Euclid: 18 July 2017

zbMATH: 1255.35120
MathSciNet: MR2892903
Digital Object Identifier: 10.11650/twjm/1500406606

Subjects:
Primary: 35A15, 35J66

Rights: Copyright © 2012 The Mathematical Society of the Republic of China

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