Existence of solutions for a Robin problem involving the \(p(x)\)-Laplace operator (Q1669215)

Summary: In this article we study the nonlinear Robin boundary-value problem \(- \Delta_{p(x)} u = f(x, u)\) in \(\Omega\), \(| \nabla u |^{p \left(x\right) - 2}(\partial u / \partial \nu) + \beta(x) \left|u\right|^{p(x) - 2} u = 0\) on \(\partial \Omega\). Using the variational method, under appropriate assumptions on \(f\), we obtain results on existence and multiplicity of solutions.