Solvability of Parametric Elliptic Systems with Variable Exponents

Anass Ouannasser; Abderrahmane El Hachimi

doi:10.2478/mjpaa-2023-0021

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Solvability of Parametric Elliptic Systems with Variable Exponents

Moroccan Journal of Pure and Applied Analysis

Volume 9 (2023): Issue 3 (September 2023)

By: Anass Ouannasser and Abderrahmane El Hachimi

Open Access

|Sep 2023

Abstract

In this paper, we study the solvability to the left of the positive infimum of all eigenvalues for some non-resonant quasilinear elliptic problems involving variable exponents. We first prove the existence of at least a weak solution for some non-variational systems by using a surjectivity result for pseudomonotone operators. Furthermore, under additional conditions, we show that the solution is unique and provide examples. Second, we deal with non-resonant gradient-type systems and obtain existence by using a variational approach.

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Articles in this issue

DOI: https://doi.org/10.2478/mjpaa-2023-0021 | Journal eISSN: 2351-8227

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Language: English

Page range: 311 - 330

Submitted on: Feb 10, 2023

Accepted on: May 29, 2023

Published on: Sep 29, 2023

Published by: Sciendo

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

()-Laplacian,

positive infimum,

weak solution,

existence and uniqueness

Related subjects:

Mathematics,

Analysis,

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics

© 2023 Anass Ouannasser, Abderrahmane El Hachimi, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 9 (2023): Issue 3 (September 2023)