We investigate the problem of existence and uniqueness of ground states at fixed mass for two families of focusing nonlinear Schrodinger equations on the line. The first family consists of NLS with power nonlinearities concentrated at a point. For such model, we prove existence and uniqueness of ground states at every mass when the nonlinearity power is L-2-subcritical and at a threshold value of the mass in the L-2-critical regime. The second family is obtained by adding a standard power nonlinearity to the previous setting. In this case, we prove existence and uniqueness at every mass in the doubly subcritical case, namely when both the powers related to the pointwise and the standard nonlinearity are subcritical. If only one power is critical, then existence and uniqueness hold only at masses lower than the critical mass associated to the critical nonlinearity. Finally, in the doubly critical case ground states exist only at critical mass, whose value results from a non-trivial interplay between the two nonlinearities. (C) 2020 Elsevier Inc. All rights reserved.

Prescribed mass ground states for a doubly nonlinear Schrodinger equation in dimension one / Boni, F; Dovetta, S. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 496:1(2021), pp. 1-16. [10.1016/j.jmaa.2020.124797]

Prescribed mass ground states for a doubly nonlinear Schrodinger equation in dimension one

Boni, F;Dovetta, S
2021

Abstract

We investigate the problem of existence and uniqueness of ground states at fixed mass for two families of focusing nonlinear Schrodinger equations on the line. The first family consists of NLS with power nonlinearities concentrated at a point. For such model, we prove existence and uniqueness of ground states at every mass when the nonlinearity power is L-2-subcritical and at a threshold value of the mass in the L-2-critical regime. The second family is obtained by adding a standard power nonlinearity to the previous setting. In this case, we prove existence and uniqueness at every mass in the doubly subcritical case, namely when both the powers related to the pointwise and the standard nonlinearity are subcritical. If only one power is critical, then existence and uniqueness hold only at masses lower than the critical mass associated to the critical nonlinearity. Finally, in the doubly critical case ground states exist only at critical mass, whose value results from a non-trivial interplay between the two nonlinearities. (C) 2020 Elsevier Inc. All rights reserved.
File in questo prodotto:
File Dimensione Formato  
2021_BD_JMAA.pdf

non disponibili

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 421.8 kB
Formato Adobe PDF
421.8 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2982548