@Article{BenAli2017,
author = "Ben Ali, Khaled and Ghanmi, Abdeljabbar and Kefi, Khaled",
title = "On the Steklov problem involving the p(x)-Laplacian with indefinite weight",
journal = "Opuscula Math.",
year = "2017",
volume = "37",
number = "6",
pages = "779--794",
doi = "http://dx.doi.org/10.7494/OpMath.2017.37.6.779",
url = "http://dx.doi.org/10.7494/OpMath.2017.37.6.779",
abstract = "Under suitable assumptions, we study the existence of a weak nontrivial solution for the following Steklov problem involving the \(p(x)\)-Laplacian \[\begin{cases}\Delta_{p(x)}u=a(x)|u|^{p(x)-2}u \quad \text{in }\Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}=\lambda V(x)|u|^{q(x)-2}u \quad \text{on }\partial \Omega.\end{cases}\] Our approach is based on min-max method and Ekeland's variational principle.",
keywords = "\(p(x)\)-Laplace operator, Steklov problem, variable exponent Sobolev spaces, variational methods, Ekeland's variational principle",
issn = "1232-9274"
}