@Article{Allaoui2015,
author = "Allaoui, Mostafa",
title = "Continuous spectrum of Steklov nonhomogeneous elliptic problem",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "6",
pages = "853--866",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.6.853",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.6.853",
abstract = "By applying two versions of the mountain pass theorem and Ekeland's variational principle, we prove three different situations of the existence of solutions for the following Steklov problem: \[\begin{aligned}\Delta_{p(x)} u&=|u|^{p(x)-2}u \phantom{\lambda} \quad\text{in}\;\Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}&= \lambda|u|^{q(x)-2}u \quad\text{on}\;\partial\Omega,\end{aligned}\] where \(\Omega \subset \mathbb{R}^N\) \((N\geq 2)\) is a bounded smooth domain and \(p,q: \overline{\Omega}\rightarrow(1,+\infty)\) are continuous functions.",
keywords = "\(p(x)\)-Laplacian, Steklov problem, critical point theorem",
issn = "1232-9274"
}