We consider the nonlinear Schrödinger equation in dimension one with a nonlinearity concentrated in a finite number of points. Detailed results on the local existence of the solution in fractional Sobolev spaces Hρare given. We also prove the conservation of the L2-norm and the energy of the solution and give a global existence result for repulsive and weakly attractive interaction in the space H1Finally we prove the existence of blow-up solutions for strongly attractive interaction. © 2001 Academic Press.

Adami, R., Teta, A. (2001). A class of nonlinear Schrodinger equations with concentrated nonlinearity. JOURNAL OF FUNCTIONAL ANALYSIS, 180(1), 148-175 [10.1006/jfan.2000.3697].

A class of nonlinear Schrodinger equations with concentrated nonlinearity

ADAMI, RICCARDO;
2001

Abstract

We consider the nonlinear Schrödinger equation in dimension one with a nonlinearity concentrated in a finite number of points. Detailed results on the local existence of the solution in fractional Sobolev spaces Hρare given. We also prove the conservation of the L2-norm and the energy of the solution and give a global existence result for repulsive and weakly attractive interaction in the space H1Finally we prove the existence of blow-up solutions for strongly attractive interaction. © 2001 Academic Press.
Articolo in rivista - Articolo scientifico
Schrodinger equations
English
148
175
Adami, R., Teta, A. (2001). A class of nonlinear Schrodinger equations with concentrated nonlinearity. JOURNAL OF FUNCTIONAL ANALYSIS, 180(1), 148-175 [10.1006/jfan.2000.3697].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/10281/18133
Citazioni
  • Scopus 39
  • ???jsp.display-item.citation.isi??? 43
Social impact