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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
Published electronically: September 1, 2010
MathSciNet review: 2745653
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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 $ n$-dimensional space and $ (n-1)$-dimensional space.

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Additional Information

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

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

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

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.