## Analysis & PDE

### The nonlinear Schrödinger equation ground states on product spaces

#### Abstract

We study the nature of the nonlinear Schrödinger equation ground states on the product spaces $ℝn×Mk$, where $Mk$ is a compact Riemannian manifold. We prove that for small $L2$ masses the ground states coincide with the corresponding $ℝn$ ground states. We also prove that above a critical mass the ground states have nontrivial $Mk$ dependence. Finally, we address the Cauchy problem issue, which transforms the variational analysis into dynamical stability results.

#### Article information

Source
Anal. PDE, Volume 7, Number 1 (2014), 73-96.

Dates
Accepted: 21 May 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513731466

Digital Object Identifier
doi:10.2140/apde.2014.7.73

Mathematical Reviews number (MathSciNet)
MR3219500

Zentralblatt MATH identifier
1294.35148

Subjects
Secondary: 37K45: Stability problems

#### Citation

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

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