Habib Maagli, Ramzi Alsaedi, Noureddine Zeddini
Abstract:
In this article, we are concerned with a class of nonlinear partial
differential elliptic equations with Dirichlet boundary data.
The key feature of this paper consists in competition effects of two
generalized differential operators, which extend the standard operators
with variable exponent. This class of problems is motivated by phenomena
arising in non-Newtonian fluids or image reconstruction, which deal with
operators and nonlinearities with variable exponents. We establish an
existence property in the framework of small perturbations of the reaction
term with indefinite potential. The mathematical analysis developed in this
paper is based on the theory of anisotropic function spaces.
Our analysis combines variational arguments with energy estimates.
Submitted June 10, 2017. Published September 19, 2017.
Math Subject Classifications: 35J20, 35P30, 46E35.
Key Words: Variable exponent; nonhomogeneous differential operator;
Ekeland variational principle; energy estimates.
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Habib Mâagli Department of Mathematics, College of Sciences and Arts King Abdulaziz University, Rabigh Campus P.O. Box 344, Rabigh 21911, Saudi Arabia email: maaglihabib@gmail.com |
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Ramzi Alsaedi Department of Mathematics Faculty of Sciences, King Abdulaziz University P.O. Box 80203, Jeddah 21589, Saudi Arabia email: ramzialsaedi@yahoo.co.uk |
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Noureddine Zeddini Department of Mathematics, Faculty of Sciences Taibah University Medina, Saudi Arabia email: noureddinezeddini@yahoo.fr |
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