Existence of positive radial solutions for a problem involving the weighted Heisenberg $ p(\cdot) $-Laplacian operator-Reference-Cited by-同舟云学术

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

Published:2023 Issue:1 Volume:8 Page:404-422
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ragusa Maria Alessandra¹,Razani Abdolrahman²,Safari Farzaneh²

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference35 articles.

1. F. Anceschi, S. Muzzioli, S. Polidoro, Existence of a fundamental solution of partial differential equations associated to Asian options, Nonlinear Anal., 62 (2021), 103373. https://doi.org/10.1016/j.nonrwa.2021.103373

2. M. Badiale, E. Serra, Semilinear Elliptic Equations for Beginners, Existence Results via the Variational Approach, Springer science and Business Media, 2010.

3. I. Birindelli, F. Ferrari, E. Valdinoci, Semilinear PDEs in the Heisenberg group: The role of the right invariant vector fields, Nonlinear Anal., 72 (2010), 987–997. https://doi.org/10.1016/j.na.2009.07.039

4. G. M. Bisci, P. Pucci, Critical Dirichlet problems on $H$ domains of Carnot groups, Two nonlinear days in Urbino 2017, Electron. J. Diff. Eqns., Special Volume dedicated to the memory of Anna Aloe, Conf., 25 (2018), 179–196.

5. W. L. Chow, Über systeme von liearren partiellen differentialgleichungen erster ordnung, Math. Ann., 117 (1940), 98–105. https://doi.org/10.1007/BF01450011

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