<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this note we prove that solutions of a φ-Laplacian operator on the entire space ℝ<sup>N</sup> are locally regular (Hölder continuous), positive and vanish at infinity. Mild restrictions are imposed on the right-hand side of the equation. For example, we assume a Lieberman-like condition but the hypothesis of differentiability is dropped. This is in striking contrast with the classical case. </p></abstract>

In this note we prove that solutions of a φ-Laplacian operator on the entire space ℝN are locally regular (Hölder continuous), positive and vanish at infinity. Mild restrictions are imposed on the right-hand side of the equation. For example, we assume a Lieberman-like condition but the hypothesis of differentiability is dropped. This is in striking contrast with the classical case.

Regularity, positivity and asymptotic vanishing of solutions of a φ-Laplacian

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Regularity, positivity and asymptotic vanishing of solutions of a φ-Laplacian"}

In this note we prove that solutions of a φ-Laplacian operator on the entire space ℝN are locally regular (Hölder continuous), positive and vanish at infinity....

Regularity, positivity and asymptotic vanishing of solutions of a φ-Laplacian

Published Online: Mar 31, 2018

Page range: 59 - 72

DOI: https://doi.org/10.1515/auom-2017-0035

Keywords
Orlicz-Sobolev space, φ-Laplacian, regularity, asymptotic vanishing

© 2018

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

Regularity, positivity and asymptotic vanishing of solutions of a φ-Laplacian

Published Online: Mar 31, 2018

Page range: 59 - 72

DOI: https://doi.org/10.1515/auom-2017-0035

KeywordsOrlicz-Sobolev space, φ-Laplacian, regularity, asymptotic vanishing

© 2018

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

Keywords
Orlicz-Sobolev space, φ-Laplacian, regularity, asymptotic vanishing