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2005 Global bifurcation branches for radially symmetric Schrödinger equations
Tobias Weth
Adv. Differential Equations 10(7): 721-746 (2005).

Abstract

We prove a new result on bifurcating branches of bound states for the nonlinear radially symmetric Schrödinger equation $$ -\Delta u =w(|x|)|u|^{\sigma}u -\lambda^2u \ \ \text{ on ${\mathbb{R}}^N$.} $$ We show that, under suitable assumptions on $w$ and $\sigma$, there exist infinitely many continua of nontrivial bound states $u_\lambda$ which emanate from the trivial solution branch at $\lambda=0$. These continua reach arbitrarily large values of $\lambda$, and they are distinguished by the number of nodal domains of the corresponding solutions $u_\lambda$.

Citation

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Tobias Weth. "Global bifurcation branches for radially symmetric Schrödinger equations." Adv. Differential Equations 10 (7) 721 - 746, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1109.35107
MathSciNet: MR2152350

Subjects:
Primary: 35J60
Secondary: 34A12, 35B32, 47J15

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 7 • 2005
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