A remark on asymptotic profiles of radial solutions with a vortex to a nonlinear Schrödinger equation

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September 2006, 5(3): 597-610. doi: 10.3934/cpaa.2006.5.597

A remark on asymptotic profiles of radial solutions with a vortex to a nonlinear Schrödinger equation

Kazuhiro Kurata ^1, and Tatsuya Watanabe ^2,

1.	Department of Mathematics and Infomation Sciences, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi,Tokyo 192-0397
2.	Department of Mathematics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi,Tokyo 192-0397, Japan

Received June 2005 Revised January 2006 Published June 2006

Abstract
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In this paper, we are concerned with radially symmetric solutions with a vortex to a nonlinear Schrödinger equation:

-ħ$^2 \Delta v+($ ħ$^2\omega^2/|x|^2+V(x))v=f(v)$ in $\mathbf R^2.$

We give precise asymptotic profiles of solutions as ħ$\rightarrow 0$ by variational methods and ODE arguments.

Keywords: Variational methods, asymptotic profiles, vortex..

Mathematics Subject Classification: 35B40, 35J20, 35Q5.

Citation: Kazuhiro Kurata, Tatsuya Watanabe. A remark on asymptotic profiles of radial solutions with a vortex to a nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2006, 5 (3) : 597-610. doi: 10.3934/cpaa.2006.5.597

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