Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator
Mostafa Allaoui, Abdelrachid El Amrouss, Anass Ourraoui · Electronic journal of qualitative theory of differential equations · 2014
In this article, we study the nonlinear Steklov boundary-value problem $$\begin{alignedat}{2} \Delta_{p(x)}u & =|u|^{p(x)-2}u \quad &&\text{in } \Omega, \\ | abla u|^{p(x)-2}\frac{\partial u}{\partial u} & = f(x,u) \quad &&\text{on } \partial\Omega. \end{alignedat}$$ We prove the existence of infinitely many non-negative solutions of the problem by applying a general variational principle due to B.\ Ricceri and the theory of the variable exponent Sobolev spaces.