Axial symmetry of some steady state solutions to nonlinear Schrödinger equations

Gui, Changfeng; Malchiodi, Andrea; Xu, Haoyuan

doi:10.1090/S0002-9939-2010-10638-X

Axial symmetry of some steady state solutions to nonlinear Schrödinger equations
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by Changfeng Gui, Andrea Malchiodi and Haoyuan Xu PDF

Proc. Amer. Math. Soc. 139 (2011), 1023-1032 Request permission

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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