On the study of $(p, Q)$-Laplace Choquard equations with critical Trudinger-Moser nonlinearity in $\mathbb{H}^N$

Fuente: arXiv
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Main Authors: Mahanta, Deepak Kumar, Mukherjee, Tuhina, Sarkar, Abhishek, Sharma, Lovelesh
Format: Preprint
Published: 2024
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_version_ 1866913442063974400
author Mahanta, Deepak Kumar
Mukherjee, Tuhina
Sarkar, Abhishek
Sharma, Lovelesh
author_facet Mahanta, Deepak Kumar
Mukherjee, Tuhina
Sarkar, Abhishek
Sharma, Lovelesh
contents This paper deals with the existence and multiplicity of nontrivial solutions for $(p, Q)$-Laplace equations with the Stein-Weiss reaction under critical exponential nonlinearity in the Heisenberg group $\mathbb{H}^N$. In addition, a weight function and two positive parameters have also been included in the nonlinearity. The developed analysis is significantly influenced by these two parameters. Further, the mountain pass theorem, the Ekeland variational principle, the Trudinger-Moser inequality, the doubly weighted Hardy-Littlewood-Sobolev inequality and a completely new Brézis-Lieb type lemma for Choquard nonlinearity play key roles in our proofs.
format Preprint
id arxiv_https___arxiv_org_abs_2407_16240
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the study of $(p, Q)$-Laplace Choquard equations with critical Trudinger-Moser nonlinearity in $\mathbb{H}^N$
Mahanta, Deepak Kumar
Mukherjee, Tuhina
Sarkar, Abhishek
Sharma, Lovelesh
Analysis of PDEs
35D30, 35J20, 35J60, 35J92, 35R03
This paper deals with the existence and multiplicity of nontrivial solutions for $(p, Q)$-Laplace equations with the Stein-Weiss reaction under critical exponential nonlinearity in the Heisenberg group $\mathbb{H}^N$. In addition, a weight function and two positive parameters have also been included in the nonlinearity. The developed analysis is significantly influenced by these two parameters. Further, the mountain pass theorem, the Ekeland variational principle, the Trudinger-Moser inequality, the doubly weighted Hardy-Littlewood-Sobolev inequality and a completely new Brézis-Lieb type lemma for Choquard nonlinearity play key roles in our proofs.
title On the study of $(p, Q)$-Laplace Choquard equations with critical Trudinger-Moser nonlinearity in $\mathbb{H}^N$
topic Analysis of PDEs
35D30, 35J20, 35J60, 35J92, 35R03
url https://arxiv.org/abs/2407.16240