TY  - JOUR
ID  - BenAli2017
LB  - BenAli2017
AU  - Ben Ali, Khaled
AU  - Ghanmi, Abdeljabbar
AU  - Kefi, Khaled
TI  - On the Steklov problem involving the p(x)-Laplacian with indefinite weight
ST  - On the Steklov problem involving the p(x)-Laplacian with indefinite weight
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 6
SP  - 779
EP  - 794
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.6.779
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.6.779
AB  - 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.
KW  - \(p(x)\)-Laplace operator
KW  - Steklov problem
KW  - variable exponent Sobolev spaces
KW  - variational methods
KW  - Ekeland's variational principle
SN  - 1232-9274
ER  -