Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 132, pp. 1-12.

Title: Existence and multiplicity of solutions for a Steklov
       problem involving the p(x)-Laplace operator

Authors: Mostafa Allaoui  (Univ. Mohamed I, Oujda, Morocco)
         Abdel Rachid El Amrouss (Univ. Mohamed I, Oujda, Morocco)
	 Anass Ourraoui   (Univ. Mohamed I, Oujda, Morocco)

Abstract:
 In this article we study the nonlinear Steklov boundary-value problem
 $$\displaylines{
  \Delta_{p(x)} u=|u|^{p(x)-2}u \quad \hbox{in } \Omega, \cr
  |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}=\lambda f(x,u) \quad
 \hbox{on } \partial\Omega.
 }$$
 Using the variational method, under appropriate assumptions on f, we obtain
 results on existence and multiplicity of solutions.

Submitted February 24, 2012. Published August 15, 2012.
Math Subject Classifications: 35J48, 35J60, 35J66
Key Words: p(x)-Laplace operator; variable exponent Lebesgue space;
           variable exponent Sobolev space; Ricceri's variational principle.