Advances in Differential Equations

An existence and stability result for standing waves of nonlinear Schrödinger equations

Louis Jeanjean and Stefan Le Coz

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Abstract

We consider a nonlinear Schrödinger equation with a nonlinearity of the form $V(x)g(u)$. Assuming that $V(x)$ behaves like $|x|^{-b}$ at infinity and $g(s)$ like $|s|^p$ around $0$, we prove the existence and orbital stability of travelling waves if $1 < p < 1+(4-2b)/N$.

Article information

Source
Adv. Differential Equations Volume 11, Number 7 (2006), 813-840.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867677

Mathematical Reviews number (MathSciNet)
MR2236583

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B35: Stability 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Jeanjean, Louis; Le Coz, Stefan. An existence and stability result for standing waves of nonlinear Schrödinger equations. Adv. Differential Equations 11 (2006), no. 7, 813--840. https://projecteuclid.org/euclid.ade/1355867677.


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