<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the present paper, we show the existence of solutions of some nonlinear inequalities of the form 〈<italic>Au</italic> + <italic>g</italic>(<italic>x</italic>, <italic>u</italic>,∇ <italic>u</italic>), <italic>v −u</italic>〉 ≥〈 <italic>f</italic>, <italic>v −u〉</italic> with gradient constraint that depend on the solution itself, where <italic>A</italic> is a Leray-Lions operator defined on Orlicz spaces, <italic>g</italic> is a nonlinearity and <italic>f ∈ L</italic><sup>1</sup>.</p></abstract>

In the present paper, we show the existence of solutions of some nonlinear inequalities of the form 〈Au + g(x, u,∇ u), v −u〉 ≥〈 f, v −u〉 with gradient constraint that depend on the solution itself, where A is a Leray-Lions operator defined on Orlicz spaces, g is a nonlinearity and f ∈ L1.

Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Some class of nonlinear inequalities with gradient constraints in Orlicz spaces"}

In the present paper, we show the existence of solutions of some nonlinear inequalities of the form 〈Au + g(x, u,∇ u), v −u〉 ≥〈 f, v −u〉 with gradient...

Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

Published Online: Oct 10, 2020

Page range: 281 - 302

Received: Jun 15, 2020

Accepted: Sep 30, 2020

DOI: https://doi.org/10.2478/mjpaa-2020-0022

Keywords
Nonlinear variational inequalities, Nonlinear elliptic equations, -Laplacian, Orlicz spaces

© 2020 S. Ajagjal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

Published Online: Oct 10, 2020

Page range: 281 - 302

Received: Jun 15, 2020

Accepted: Sep 30, 2020

DOI: https://doi.org/10.2478/mjpaa-2020-0022

KeywordsNonlinear variational inequalities, Nonlinear elliptic equations, -Laplacian, Orlicz spaces

© 2020 S. Ajagjal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Nonlinear variational inequalities, Nonlinear elliptic equations, -Laplacian, Orlicz spaces