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.