Vol. 295, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
The Journal
Editorial Board
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
This article is available for purchase or by subscription. See below.
Classification of positive smooth solutions to third-order PDEs involving fractional Laplacians

Wei Dai and Guolin Qin

Vol. 295 (2018), No. 2, 367–383

In this paper, we are concerned with the third-order equations

(Δ)3 2 u = ud+3 d3 ,x d, u C3(d), u(x) > 0,x d,


(Δ)3 2 u =( 1 |x|6 |u|2)u,x d, u C3(d), u(x) > 0,x d,d 7,

with 3 2 -critical nonlinearity. By showing the equivalence between the PDEs and the corresponding integral equations and using results from Chen et al. (2006) and Dai et al. (2018), we prove that positive classical solutions u to the above equations are radially symmetric about some point x0 d and derive the explicit forms for u.

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:

fractional Laplacians, odd order, positive smooth solutions, radial symmetry, uniqueness, equivalence
Mathematical Subject Classification 2010
Primary: 35R11
Secondary: 35B06, 35J91
Received: 21 July 2017
Revised: 31 January 2018
Accepted: 3 February 2018
Published: 11 April 2018
Wei Dai
School of Mathematics and Systems Science
Beihang University (BUAA)
Guolin Qin
School of Mathematics and Systems Science
Beihang University (BUAA)