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2000 On interacting bumps of semi-classical states of nonlinear Schrödinger equations
Xiaosong Kang, Juncheng Wei
Adv. Differential Equations 5(7-9): 899-928 (2000). DOI: 10.57262/ade/1356651291

Abstract

We study concentrated positive bound states of the following nonlinear Schr\"odinger equation: \[ h^2 \Delta u - V(x) u + u^p=0,\ \ \ u>0, \ \ x \in R^N , \] where $ p$ is subcritical. We prove that, at a local maximum point $x_0$ of the potential function $V(x)$ and for arbitrary positive integer $K (K>1)$, there always exist solutions with $K$ interacting bumps concentrating near $x_0$. We also prove that at a nondegenerate local minimum point of $V(x) $ such solutions do not exist.

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Xiaosong Kang. Juncheng Wei. "On interacting bumps of semi-classical states of nonlinear Schrödinger equations." Adv. Differential Equations 5 (7-9) 899 - 928, 2000. https://doi.org/10.57262/ade/1356651291

Information

Published: 2000
First available in Project Euclid: 27 December 2012

zbMATH: 1217.35065
MathSciNet: MR1776345
Digital Object Identifier: 10.57262/ade/1356651291

Subjects:
Primary: 35J60
Secondary: 35A05 , 35B50 , 35Q55

Rights: Copyright © 2000 Khayyam Publishing, Inc.

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Vol.5 • No. 7-9 • 2000
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