Title: Nonlinear Steklov eigenvalue problem with variable exponents and without Ambrosetti-Rabinowitz condition

Authors: Abdellah Zerouali; Belhadj Karim; Omar Chakrone

Addresses: Regional Centre of Trades Education and Training, Oujda, Morocco ' University Moulay Ismail, Faculty of Sciences and Technics, Errachidia, Morocco ' University Mohamed I, Faculty of Sciences, Oujda, Morocco

Abstract: In this paper, we study a nonlinear Steklov eigenvalue problem involving the p(x)-Laplacian on a bounded domain. We introduce a new variational technic that allows us to investigate this problem without need of the Ambrosetti-Rabinowitz condition on the nonlinearity.

Keywords: critical point; p(x)-Laplacian; Steklov problem; variable exponent Lebesgue-Sobolev spaces.

DOI: 10.1504/IJDSDE.2018.089102

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.1/2, pp.113 - 122

Received: 21 Jun 2016
Accepted: 02 Aug 2017
Published online: 05 Jan 2018 *

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