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), 10231032
MSC (2010):
Primary 35J15, 35J20, 35J60, 35J61
Published electronically:
September 1, 2010
MathSciNet review:
2745653
Fulltext PDF
Abstract 
References 
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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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 J. Busca and P. Felmer, Qualitative properties of some bounded positive solutions to scalar field equations. Calc. Var. Partial Differential Equations 13 (2001) pp. 191211. MR 1861097 (2002g:35063)
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 E. N. Dancer, On the uniqueness of the positive solution of a singularly perturbed problem, Rocky Mountain Journal of Mathematics 25 (1995) pp. 957975. MR 1357103 (96j:35021)
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 E. N. Dancer, New solutions of equations on , Annali Della Scuola Normale Superiore di Pisa 30 (2001) pp. 535563. MR 1896077 (2003g:35057)
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 M. Del Pino, M. Kowalzyck, F. Pacard and J. Wei, The Toda system and multipleend solutions of autonomous planar elliptic problems, preprint, 2007.
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 Changfeng Gui, Hamiltonian identities for elliptic partial differential equations, Journal of Functional Analysis 254 (2008), no. 4, pp. 904933. MR 2381198 (2009b:35112)
 6.
 Changfeng Gui, Hamiltonian constants for several new entire solutions, Front. Math. China 3 (2008) pp. 195204. MR 2395216 (2009e:35075)
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 C. Gui, Symmetry of traveling wave solutions to the AllenCahn equation in , preprint.
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 C. Gui, Symmetry of certain saddle solutions to the AllenCahn equation, preprint.
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 Andrea Malchiodi, Some new entire solutions of semilinear elliptic equations on , preprint, 2007.
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Additional Information
Changfeng Gui
Affiliation:
Department of Mathematics, U9, University of Connecticut Storrs, Connecticut 06269
Email:
gui@math.uconn.edu
Andrea Malchiodi
Affiliation:
Sector of Mathematical Analysis, SISSA, Via Beirut 24, 34014 Trieste, Italy
Email:
malchiod@sissa.it
Haoyuan Xu
Affiliation:
Department of Mathematics, U9, University of Connecticut, Storrs, Connecticut 06269
Email:
haoyuan@math.uconn.edu
DOI:
http://dx.doi.org/10.1090/S00029939201010638X
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.
