Properties for Nonlinear Fractional SubLaplace Equations on the Heisenberg Group

sci, Xinjing Wang and Pengcheng Niu

doi:10.4208/jpde.v32.n1.5

JPDE

2019

DOI: 10.4208/jpde.v32.n1.5

|View full text |Cite

Properties for Nonlinear Fractional SubLaplace Equations on the Heisenberg Group

Xinjing Wang and Pengcheng Niu sci¹

Abstract: The aim of the paper is to study properties of solutions to the nonlinear fractional subLaplace equations on the Heisenberg group. Based on the method of moving planes to the Heisenberg group, we prove the Liouville property of solutions on a half space and the symmetry and monotonicity of the solutions on the whole group respectively. AMS Subject Classifications: 35A01, 35J57, 35D99Chinese Library Classifications: O175.2

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Compact embeddings, eigenvalue problems, and subelliptic Brezis–Nirenberg equations involving singularity on stratified Lie groups

2023

View full text Add to dashboard Cite

The purpose of this paper is twofold: first we study an eigenvalue problem for the fractional p-sub-Laplacian over the fractional Folland–Stein–Sobolev spaces on stratified Lie groups. We apply variational methods to investigate the eigenvalue problems. We conclude the positivity of the first eigenfunction via the strong minimum principle for the fractional p-sub-Laplacian. Moreover, we deduce that the first eigenvalue is simple and isolated. Secondly, utilising established properties, we prove the existence of at least two weak solutions via the Nehari manifold technique to a class of subelliptic singular problems associated with the fractional p-sub-Laplacian on stratified Lie groups. We also investigate the boundedness of positive weak solutions to the considered problem via the Moser iteration technique. The results obtained here are also new even for the case $$p=2$$ p = 2 with $$\mathbb {G}$$ G being the Heisenberg group.

show abstract

Compact embeddings, eigenvalue problems, and subelliptic Brezis–Nirenberg equations involving singularity on stratified Lie groups

2023

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Properties for Nonlinear Fractional SubLaplace Equations on the Heisenberg Group

Cited by 1 publication

References 17 publications

Compact embeddings, eigenvalue problems, and subelliptic Brezis–Nirenberg equations involving singularity on stratified Lie groups

Compact embeddings, eigenvalue problems, and subelliptic Brezis–Nirenberg equations involving singularity on stratified Lie groups

Contact Info

Product

Resources

About