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October 2020 Uniqueness of the ground state of the NLS on $\mathbb{H}^d$ via analytical and topological methods
Alessandro Maria Selvitella
Rocky Mountain J. Math. 50(5): 1817-1832 (October 2020). DOI: 10.1216/rmj.2020.50.1817

Abstract

We give an analytical and topological proof of the uniqueness of the ground state of the nonlinear Schrödinger equation defined on the Hyperbolic space d when the power type nonlinearity has H1(d)-subcritical exponent (1<p<1+4(d2) for d3 and 1<p<+ for d=2) and the phase λ is positive. Differently from what it is available in the literature, we use the polar model of d and we do not take advantage of the dual Euclidean problem. Our proof of uniqueness uses the shooting method, some new monotonicity formulas and the geometry of the potential energy.

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Alessandro Maria Selvitella. "Uniqueness of the ground state of the NLS on $\mathbb{H}^d$ via analytical and topological methods." Rocky Mountain J. Math. 50 (5) 1817 - 1832, October 2020. https://doi.org/10.1216/rmj.2020.50.1817

Information

Received: 16 January 2020; Revised: 10 February 2020; Accepted: 10 February 2020; Published: October 2020
First available in Project Euclid: 5 November 2020

zbMATH: 07274839
MathSciNet: MR4170691
Digital Object Identifier: 10.1216/rmj.2020.50.1817

Subjects:
Primary: 35J61, 35Q55, 58J05

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 5 • October 2020
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