<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Solvability of Parametric Elliptic Systems with Variable Exponents

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Solvability of Parametric Elliptic Systems with Variable Exponents"}

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...

Solvability of Parametric Elliptic Systems with Variable Exponents

Published Online: Sep 29, 2023

Page range: 311 - 330

Received: Feb 10, 2023

Accepted: May 29, 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0021

Keywords
()-Laplacian, positive infimum, weak solution, existence and uniqueness

© 2023 Anass Ouannasser et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Solvability of Parametric Elliptic Systems with Variable Exponents

Published Online: Sep 29, 2023

Page range: 311 - 330

Received: Feb 10, 2023

Accepted: May 29, 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0021

Keywords()-Laplacian, positive infimum, weak solution, existence and uniqueness

© 2023 Anass Ouannasser et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
()-Laplacian, positive infimum, weak solution, existence and uniqueness