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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.4 Antofagasta dic. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-04-0048 

Articles

Nonlinear elliptic problems in weighted variable exponent Sobolev spaces by topological degree

Mustapha Ait Hammou1 
http://orcid.org/0000-0002-3930-3469

El Houssine Azroul2 

1University Sidi Mohamed Ben Abdellah, FSDM, Fez, Morocco, e-mail: mus.aithammou@gmail.com

2 University Sidi Mohamed Ben Abdellah, FSDM, Fez, Morocco, e-mail: azroulelhoussine@gmail.com

Abstract

In this paper, we prove the existence of solutions for the nonlinear p(·)-degenerate problems involving nonlinear operators of the form − div a(x, ∇u) = f(x, u, ∇u) where a and f are Carathéodory functions satisfying some nonstandard growth conditions.

Keywords: Nonlinear elliptic equation; Weighted Sobolev spaces with variable exponent; Dirichlet problem.

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Received: July 2018; Accepted: March 2019

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