We consider the Schrödinger equation in R3 with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V, which is strictly larger than the standard H1-space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions. © 2003 Éditions scientifiques et médicales Elsevier SAS.

Adami, R., Dell'Antonio, G., Figari, R., Teta, A. (2003). The Cauchy problem for the Schrodinger equation in dimension three with concentrated nonlinearity. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 20(3), 447-500 [10.1016/S0294-1449(02)00022-7].

The Cauchy problem for the Schrodinger equation in dimension three with concentrated nonlinearity

ADAMI, RICCARDO;
2003

Abstract

We consider the Schrödinger equation in R3 with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V, which is strictly larger than the standard H1-space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions. © 2003 Éditions scientifiques et médicales Elsevier SAS.
Articolo in rivista - Articolo scientifico
Schrodinger equations
English
447
500
Adami, R., Dell'Antonio, G., Figari, R., Teta, A. (2003). The Cauchy problem for the Schrodinger equation in dimension three with concentrated nonlinearity. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 20(3), 447-500 [10.1016/S0294-1449(02)00022-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/18179
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