Vol. 305, No. 2, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Singular periodic solutions to a critical equation in the Heisenberg group

Claudio Afeltra

Vol. 305 (2020), No. 2, 385–406
DOI: 10.2140/pjm.2020.305.385
Abstract

We construct positive solutions to the equation

Δnu = uQ+2 Q2

on the Heisenberg group, singular in the origin, similar to the Fowler solutions of the Yamabe equations on n. These satisfy the homogeneity property u δT = T(Q2)2u for some T large enough, where Q = 2n + 2 and δT is the natural dilation in n. We use the Lyapunov–Schmidt method applied to a family of approximate solutions built by periodization from the global regular solution classified by Jerison and Lee (1988).

Keywords
subelliptic equations, perturbation methods
Mathematical Subject Classification 2010
Primary: 35H20, 35J20, 35J61, 35R03
Milestones
Received: 6 August 2019
Accepted: 11 October 2019
Published: 29 April 2020
Authors
Claudio Afeltra
Scuola Normale Superiore
Pisa
Italy