Opuscula Mathematica
Opuscula Math. 37, no. 6 (), 779-794
http://dx.doi.org/10.7494/OpMath.2017.37.6.779
Opuscula Mathematica

On the Steklov problem involving the p(x)-Laplacian with indefinite weight




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.
Mathematics Subject Classification: 35J48, 35J66.
Cite this article as:
Khaled Ben Ali, Abdeljabbar Ghanmi, Khaled Kefi, On the Steklov problem involving the p(x)-Laplacian with indefinite weight, Opuscula Math. 37, no. 6 (2017), 779-794, http://dx.doi.org/10.7494/OpMath.2017.37.6.779
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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