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In this article we study the nonlinear Steklov boundary-value problem ∆p(x)u = |u|p(x)−2u in Ω, |∇u|p(x)−2 ∂u ∂ν = λf(x, u) on ∂Ω. Using the variational method, under appropriate assumptions on f , we obtain results on existence and multiplicity of solutions.
In this article, we study the nonlinear Steklov boundary-value problem ∆p(x)u = |u|p(x)−2u in Ω, |∇u|p(x)−2 ∂u ∂ν = f (x, u) on ∂Ω. 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.
We study the existence of weak solutions for a parametric Robin problem driven by the p(x)-Laplacian. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with adequate variational methods and the Mountain Pass Theorem.
This paper shows the existence of at least three solutions for Navier problem involving the p(x)-biharmonic operator. Our technical approach is based on a theorem obtained by B. Ricceri.