Existence of solutions for p-sub-Laplacians with nonlinear sources on the Heisenberg group

Aidyn Kassymov; Durvudkhan Suragan

doi:10.1080/17476933.2020.1731737

Existence of solutions for p-sub-Laplacians with nonlinear sources on the Heisenberg group

Aidyn Kassymov, Durvudkhan Suragan

Nazarbayev University

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this note, we prove the existence of a weak solution for nonlinear p-sub-Laplacian equations with the Dirichlet boundary condition on the Heisenberg group. In the proof, we use a version of the mountain pass theorem and the Folland–Stein embedding theorem as the main tools.

Original language	English
Pages (from-to)	614-625
Number of pages	12
Journal	Complex Variables and Elliptic Equations
Volume	66
Issue number	4
DOIs	https://doi.org/10.1080/17476933.2020.1731737
Publication status	Published - 2021

Keywords

22E30
35A01
35H99
B. Zhang
Existence
Heisenberg group
mountain pass theorem
p-sub-Laplacian

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1080/17476933.2020.1731737

Cite this

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title = "Existence of solutions for p-sub-Laplacians with nonlinear sources on the Heisenberg group",

abstract = "In this note, we prove the existence of a weak solution for nonlinear p-sub-Laplacian equations with the Dirichlet boundary condition on the Heisenberg group. In the proof, we use a version of the mountain pass theorem and the Folland–Stein embedding theorem as the main tools.",

keywords = "22E30, 35A01, 35H99, B. Zhang, Existence, Heisenberg group, mountain pass theorem, p-sub-Laplacian",

author = "Aidyn Kassymov and Durvudkhan Suragan",

note = "Funding Information: This work was supported in parts by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. The first author was also supported in parts by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and AP08052001 MESRK Grant. Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor & Francis Group. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

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T1 - Existence of solutions for p-sub-Laplacians with nonlinear sources on the Heisenberg group

AU - Kassymov, Aidyn

AU - Suragan, Durvudkhan

N1 - Funding Information: This work was supported in parts by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. The first author was also supported in parts by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and AP08052001 MESRK Grant. Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - In this note, we prove the existence of a weak solution for nonlinear p-sub-Laplacian equations with the Dirichlet boundary condition on the Heisenberg group. In the proof, we use a version of the mountain pass theorem and the Folland–Stein embedding theorem as the main tools.

AB - In this note, we prove the existence of a weak solution for nonlinear p-sub-Laplacian equations with the Dirichlet boundary condition on the Heisenberg group. In the proof, we use a version of the mountain pass theorem and the Folland–Stein embedding theorem as the main tools.

KW - 22E30

KW - 35A01

KW - 35H99

KW - B. Zhang

KW - Existence

KW - Heisenberg group

KW - mountain pass theorem

KW - p-sub-Laplacian

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SP - 614

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JO - Complex Variables and Elliptic Equations

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ER -

Existence of solutions for p-sub-Laplacians with nonlinear sources on the Heisenberg group

Abstract

Keywords

ASJC Scopus subject areas

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