Advances in Differential Equations

Global bifurcation branches for radially symmetric Schrödinger equations

Tobias Weth

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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 $u_\lambda$.

Article information

Source
Adv. Differential Equations Volume 10, Number 7 (2005), 721-746.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867829

Mathematical Reviews number (MathSciNet)
MR2152350

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 35B32: Bifurcation [See also 37Gxx, 37K50] 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]

Citation

Weth, Tobias. Global bifurcation branches for radially symmetric Schrödinger equations. Adv. Differential Equations 10 (2005), no. 7, 721--746. https://projecteuclid.org/euclid.ade/1355867829.


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