Existence of positive radial solutions for a problem involving the weighted Heisenberg $ p(\cdot) $-Laplacian operator

Maria Alessandra Ragusa; Abdolrahman Razani; Farzaneh Safari; Maria Alessandra Ragusa; Abdolrahman Razani; Farzaneh Safari

doi:10.3934/math.2023019

AIMS Mathematics

2023, Volume 8, Issue 1: 404-422. doi: 10.3934/math.2023019

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Research article

Existence of positive radial solutions for a problem involving the weighted Heisenberg $ p(\cdot) $-Laplacian operator

1.
Dipartimento di Matematica e Informatica, Università di Catania, Italy
2.
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Postal code 3414896818, Qazvin, Iran

Received: 01 July 2022 Revised: 16 September 2022 Accepted: 23 September 2022 Published: 08 October 2022
MSC : 35R03, 35B65, Secondary 35J60, 35J70

A variational principle is applied to examine a Muckenhoupt weighted $ p(\cdot) $-Laplacian equation on the Heisenberg groups. The existence of at least one positive radial solution to the problem under the Dirichlet boundary condition belongs to the first order Heisenberg-Sobolev spaces is proved.
- Heisenberg $ p(\cdot) $-Laplacian operator,
- variational principle,
- Muckenhoupt weight function,
- mountain pass geometry theorem
Citation: Maria Alessandra Ragusa, Abdolrahman Razani, Farzaneh Safari. Existence of positive radial solutions for a problem involving the weighted Heisenberg $ p(\cdot) $-Laplacian operator[J]. AIMS Mathematics, 2023, 8(1): 404-422. doi: 10.3934/math.2023019

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Abstract

A variational principle is applied to examine a Muckenhoupt weighted $ p(\cdot) $-Laplacian equation on the Heisenberg groups. The existence of at least one positive radial solution to the problem under the Dirichlet boundary condition belongs to the first order Heisenberg-Sobolev spaces is proved.

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