Vol. 13, No. 3, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 9, 1989–2240
Issue 8, 1745–1988
Issue 7, 1485–1744
Issue 6, 1289–1483
Issue 5, 1089–1288
Issue 4, 891–1088
Issue 3, 613–890
Issue 2, 309–612
Issue 1, 1–308

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Isolated singularities for semilinear elliptic systems with power-law nonlinearity

Marius Ghergu, Sunghan Kim and Henrik Shahgholian

Vol. 13 (2020), No. 3, 701–739

We study the system Δu = |u|α1u with 1 < α n+2 n2, where u = (u1,,um), m 1, is a C2 nonnegative function that develops an isolated singularity in a domain of n , n 3. Due to the multiplicity of the components of u, we observe a new Pohozaev invariant different than the usual one in the scalar case. Aligned with the classical theory of the scalar equation, we classify the solutions on the whole space as well as the punctured space, and analyze the exact asymptotic behavior of local solutions around the isolated singularity. On a technical level, we adopt the method of moving spheres and the balanced-energy-type monotonicity functionals.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

elliptic system, isolated singularity, asymptotic behavior, Pohozaev invariant
Mathematical Subject Classification 2010
Primary: 35J61
Secondary: 35J75, 35B40, 35C20
Received: 25 April 2018
Revised: 22 January 2019
Accepted: 13 March 2019
Published: 15 April 2020
Marius Ghergu
School of Mathematics and Statistics
University College Dublin
Institute of Mathematics Simion Stoilow of the Romanian Academy
Sunghan Kim
Department of Mathematical Sciences
Seoul National University
South Korea
Henrik Shahgholian
Department of Mathematics
Royal Institute of Technology