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

Abstract

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

Keywords

• p(x)-Laplace operator
• variable exponent Lebesgue space
• variable exponent Sobolev space
• Ricceri's variational principle