## Taiwanese Journal of Mathematics

### MULTIPLICITY RESULTS FOR A NEUMANN BOUNDARY VALUE PROBLEM INVOLVING THE $P(X)$-LAPLACIAN

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 16, Number 2 (2012), 621-634.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406606

Digital Object Identifier
doi:10.11650/twjm/1500406606

Mathematical Reviews number (MathSciNet)
MR2892903

Zentralblatt MATH identifier
1255.35120

#### Citation

Cammaroto, F.; Vilasi, L. MULTIPLICITY RESULTS FOR A NEUMANN BOUNDARY VALUE PROBLEM INVOLVING THE $P(X)$-LAPLACIAN. Taiwanese J. Math. 16 (2012), no. 2, 621--634. doi:10.11650/twjm/1500406606. https://projecteuclid.org/euclid.twjm/1500406606

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