Opuscula Math. 37, no. 6 (2017), 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

Khaled Ben Ali
Abdeljabbar Ghanmi
Khaled Kefi

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.

Full text (pdf)

  • Khaled Ben Ali
  • Jazan Technical College, P.O. Box: 241 Jazan 45952, Saudi Arabia
  • University of Tunis El Manar, Faculty of Sciences, 1060 Tunis, Tunisia
  • Abdeljabbar Ghanmi
  • University of Jeddah, Faculty of Science and Arts, Mathematics Department, Khulais, Saudi Arabia
  • University of Tunis El Manar, Faculty of Sciences, 1060 Tunis, Tunisia
  • Khaled Kefi
  • Northern Border University, Community College of Rafha, Saudi Arabia
  • University of Tunis El Manar, Faculty of Sciences, 1060 Tunis, Tunisia
  • Communicated by Vicentiu D. Radulescu.
  • Received: 2017-01-06.
  • Revised: 2017-01-19.
  • Accepted: 2017-01-28.
  • Published online: 2017-09-28.
Opuscula Mathematica - cover

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

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.