%0 Journal Article
%T Existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplace operator
%A Mostafa Allaoui
%A Abdel Rachid El Amrouss
%A Anass Ourraoui
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X In this article we study the nonlinear Steklov boundary-value problem $$displaylines{ Delta_{p(x)} u=|u|^{p(x)-2}u quad hbox{in } Omega, cr | abla u|^{p(x)-2}frac{partial u}{partial u}=lambda f(x,u) quad hbox{on } partialOmega. }$$ Using the variational method, under appropriate assumptions on f, we obtain results on existence and multiplicity of solutions.
%K p(x)-Laplace operator
%K variable exponent Lebesgue space
%K variable exponent Sobolev space
%K Ricceri's variational principle
%U http://ejde.math.txstate.edu/Volumes/2012/132/abstr.html