Axial symmetry of some steady state solutions to nonlinear Schrödinger equations

Authors:
Changfeng Gui, Andrea Malchiodi and Haoyuan Xu

Journal:
Proc. Amer. Math. Soc. **139** (2011), 1023-1032

MSC (2010):
Primary 35J15, 35J20, 35J60, 35J61

DOI:
https://doi.org/10.1090/S0002-9939-2010-10638-X

Published electronically:
September 1, 2010

MathSciNet review:
2745653

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of -dimensional space and -dimensional space.

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Additional Information

**Changfeng Gui**

Affiliation:
Department of Mathematics, U-9, University of Connecticut Storrs, Connecticut 06269

Email:
gui@math.uconn.edu

**Andrea Malchiodi**

Affiliation:
Sector of Mathematical Analysis, SISSA, Via Beirut 2-4, 34014 Trieste, Italy

Email:
malchiod@sissa.it

**Haoyuan Xu**

Affiliation:
Department of Mathematics, U-9, University of Connecticut, Storrs, Connecticut 06269

Email:
haoyuan@math.uconn.edu

DOI:
https://doi.org/10.1090/S0002-9939-2010-10638-X

Keywords:
Nonlinear Schrödinger equation,
steady state solution,
Hamiltonian identity,
axial symmetry,
the moving plane method

Received by editor(s):
March 28, 2010

Published electronically:
September 1, 2010

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.