Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 158, pp. 1-12.
Title: Existence of solutions for a Neumann problem involving
the p(x)-Laplacian
Authors: Giuseppina Barletta (Univ. degli Studi Mediterranea di Reggio Calabria, Italy)
Antonia Chinni (Univ. of Messina, Messina, Italy}
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 $0^+$,
we obtain an interval such that when a parameter $\lambda$
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.