Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 158, pp. 1-12.
Existence of solutions for a Neumann problem involving
the p(x)-Laplacian
Giuseppina Barletta, Antonia Chinni
Abstract:
We study the existence and multiplicity of weak solutions
for a parametric Neumann problem driven by the p(x)-Laplacian.
Under a suitable condition on the behavior of the potential at
,
we obtain an interval such that when a parameter
is in this interval, our problem admits at least one nontrivial weak solution.
We show the multiplicity of solutions for potentials
satisfying also the Ambrosetti-Rabinowitz condition. Moreover,
if the right-hand side f satisfies the Ambrosetti-Rabinowitz condition,
then we obtain the existence of two nontrivial weak solutions.
Submitted March 29, 2013. Published July 10, 2013.
Math Subject Classifications: 35J60, 35J20.
Key Words: p(x)-Laplacian; variable exponent Sobolev spaces.
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Giuseppina Barletta
Università degli Studi Mediterranea di Reggio Calabria
MECMAT-Dipartimento di Meccanica e Materiali, Via Graziella
Località Feo di Vito, 89100 Reggio Calabria, Italy
email: giuseppina.barletta@unirc.it
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Antonia Chinnì
Department of Civil, Information Technology, Construction,
Environmental Engineering and Applied Mathematics
University of Messina, 98166 Messina, Italy
email: achinni@unime.it
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