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Remarks on comparison principles for $p$ $p$ -Laplacian with extension to $(p, q)$ $(p, q)$ -Laplacian

Ahmed Mohammed

https://orcid.org/0000-0001-5727-3614

Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306, USA

E-mail Address: amohammed@bsu.edu

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and

Antonio Vitolo

https://orcid.org/0000-0001-6300-7953

Dipartimento di Matematica, Università di Salerno, 84084 Fisciano (Salerno), Italy

E-mail Address: vitolo@unisa.it

Corresponding author.

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https://doi.org/10.1142/S1664360724500115Cited by:1 (Source: Crossref)

Abstract

Our purpose is to generalize some recent comparison principles for operators driven by $p$ $p$ -Laplacian to a wide class of quasilinear equations including $(p, q)$ $(p, q)$ -Laplacian. It turns out, in particular, that adding a $q$ $q$ -Laplacian to $p$ $p$ -Laplacian allows to weaken the assumptions needed on the Hamiltonian of lower order terms. The results are specialized in the case that the Hamiltonian has at most polynomial growth in the gradient with coefficients depending on $x$ $x$ and $u$ $u$ .

Communicated by Vicentiu Radulescu

Keywords:

AMSC: 35J62, 35B50, 35B51

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Vol. 14, No. 03

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History

Received 19 September 2024

Revised 4 October 2024

Accepted 10 October 2024

Published: 30 November 2024

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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