Existence Result for a Double Phase Problem Involving the (p(x), q(x))-Laplacian Operator-Reference-Cited by-同舟云学术

Existence Result for a Double Phase Problem Involving the (p(x), q(x))-Laplacian Operator

Published:2023-08-01 Issue:4 Volume:73 Page:969-982
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Ouaarabi Mohamed El¹,Allalou Chakir¹,Melliani Said¹

Affiliation:

1. Applied Mathematics and Scientific Computing Laboratory, Faculty of Science and Technics, Sultan Moulay Slimane University , Slimane , MOROCCO , mohamed.elouaarabi@usms.ma

Abstract

ABSTRACT The Dirichlet boundary value problem for elliptic equations involving the (p(x), q(x))-Laplacian operator with a reaction term depending on the gradient and on two real parameters is considered in this paper. Using the topological degree theory for a class of demicontinuous operators of generalized (S +) and the theory of the variable exponent Sobolev spaces, we prove the existence of at least one weak solution of such problem.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2023-0072/pdf

Reference28 articles.

1. ABOULAICH, R.—MESKINE, D.—SOUISSI, A.: New diffusion models in image processing, Comput. Math. Appl. 56 (2008), 874–882.

2. ACERBI, E.—MINGIONE, G.: Regularity results for a class of functionals with nonstandard growth, Arch. Ration. Mech. Anal. 156 (2001), 121–140.

3. ALSAEDI, R.: Perturbed subcritical Dirichlet problems with variable exponents, Electron. J. Differential Equations 295 (2016), 1–12.

4. ANTONTSEV, S.—SHMAREV, S.: A model porous medium equation with variable exponent of nonlinearity: Existence, uniqueness and localization properties of solutions, Nonlinear Anal. 60 (2005), 515–545.

5. BAHROUNI, A.—RADULESCU, V. D.—REPOVS, D. D.: Double phase transonic flow problems with variable growth: Nonlinear patterns and stationary waves, Nonlinearity 32(7) (2019), 2481–2495.