Analysis & PDE
- Anal. PDE
- Volume 7, Number 1 (2014), 73-96.
The nonlinear Schrödinger equation ground states on product spaces
We study the nature of the nonlinear Schrödinger equation ground states on the product spaces , where is a compact Riemannian manifold. We prove that for small masses the ground states coincide with the corresponding ground states. We also prove that above a critical mass the ground states have nontrivial dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results.
Anal. PDE, Volume 7, Number 1 (2014), 73-96.
Received: 2 May 2012
Accepted: 21 May 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 37K45: Stability problems
Terracini, Susanna; Tzvetkov, Nikolay; Visciglia, Nicola. The nonlinear Schrödinger equation ground states on product spaces. Anal. PDE 7 (2014), no. 1, 73--96. doi:10.2140/apde.2014.7.73. https://projecteuclid.org/euclid.apde/1513731466