Energy convexityestimates for  non-degenerate ground states of  nonlinear 1D Schrödinger systems

Eugenio Montefusco; Benedetta Pellacci; Marco Squassina

doi:10.3934/cpaa.2010.9.867

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2010, Volume 9, Issue 4: 867-884. Doi: 10.3934/cpaa.2010.9.867

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Energy convexity estimates for non-degenerate ground states of nonlinear 1D Schrödinger systems

1.
Dipartimento di Matematica, Sapienza Università di Roma, Piazzale A. Moro 5, 00185 Roma
2.
Dipartimento di Scienze Applicate, Università degli Studi di Napoli Parthenope, CDN Isola C4, I-80143 Napoli
3.
Dipartimento di Informatica, Università degli Studi di Verona, Cá Vignal 2, Strada Le Grazie 15, I-37134 Veron

Received: September 30, 2008

Revised: January 31, 2010

Published: June 2010

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Abstract

We study the spectral structure of the complex linearized operator for a class of nonlinear Schrödinger systems, obtaining as byproduct some interesting properties of non-degenerate ground state of the associated elliptic system, such as being isolated and orbitally stable.

Keywords:

Weakly coupled nonlinear Schrödinger systems,
orbital stability,
ground state solutions,
nondegeneracy of ground states.

Mathematics Subject Classification: 34B18, 34G20, 35Q55.

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Energy convexity estimates for non-degenerate ground states of nonlinear 1D Schrödinger systems

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