Existence result for a Steklov problem involving a singular nonlinearity and variable exponents

Author:

Ouerghi Haikel1,Ali Khaled Ben2,Drissi Amor3

Affiliation:

1. Department of Quantitative Methods , Jendouba University , Avenue of the Arab Maghreb Union 8189 , Jendouba , Tunisia

2. Department of Mathematics , Faculty of Sciences of Gabes, Research Laboratory of Mathematics and Applications , University of Gabes , LR17ES11, 6072 Gabes , Tunisia

3. Department of Mathematics , Faculty of Sciences Tunis El Manar , University of Tunis El Manar , 2092 Campus Universitaire , Tunis , Tunisia

Abstract

Abstract In this paper, we use the variational method to study some singular Steklov-type problem with variable exponents. More precisely, we use the min-max method in order to prove the existence of a solution to such a problem.

Publisher

Walter de Gruyter GmbH

Reference51 articles.

1. G. A. Afrouzi, A. Hadjian and S. Heidarkhani, Steklov problems involving the p ⁢ ( x ) p(x) -Laplacian, Electron. J. Differential Equations (2014), Paper No. 134.

2. K. B. Ali, Existence results for Steklov problem involving the p ⁢ ( x ) p(x) -Laplace operator, Complex Var. Elliptic Equ. 63 (2018), no. 12, 1675–1686.

3. M. Allaoui, Continuous spectrum of Steklov nonhomogeneous elliptic problem, Opuscula Math. 35 (2015), no. 6, 853–866.

4. M. Allaoui, A. R. El Amrouss and A. Ourraoui, Existence and multiplicity of solutions for a Steklov problem involving the P ⁢ ( X ) P(X) -Laplace operator, Electron. J. Differential Equations 2012 (2012), Paper No. 132.

5. S. N. Antontsev and S. I. Shmarev, A model porous medium equation with variable exponent of nonlinearity: Existence, uniqueness and localization properties of solutions, Nonlinear Anal. 60 (2005), no. 3, 515–545.

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