Existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplace operator - Mostafa Allaoui; Abdel Rachid El Amrouss; Anass Ourraoui (Electronic Journal of Differential Equations, 2012)
In this article we study the nonlinear Steklov boundary-value problem $$displaylines{ Delta_{p(x)} u=|u|^{p(x)-2}u quad hboxin Omega, cr |abla u|^{p(x)-2}fracpartial upartial u=lambda f(x,u) quad hboxon partialOmega. }$$ Using the variational method, under appropriate assumptions on f, we obtain results on existence and multiplicity of solutions.