TY  - JOUR
ID  - Allaoui2015
LB  - Allaoui2015
AU  - Allaoui, Mostafa
TI  - Continuous spectrum of Steklov nonhomogeneous elliptic problem
ST  - Continuous spectrum of Steklov nonhomogeneous elliptic problem
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 6
SP  - 853
EP  - 866
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.6.853
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.6.853
AB  - 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.
KW  - \(p(x)\)-Laplacian
KW  - Steklov problem
KW  - critical point theorem
SN  - 1232-9274
ER  -