We consider the Schrodinger equation in R-3 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 H-1-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.
The cauchy problem for the schroedinger equation in dimension three with concentrated nonlinearity / Adami, Riccardo; Dell'Antonio, Gianfausto; Figari, Rodolfo; Teta, Alessandro. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 20:3(2003), pp. 477-500. [10.1016/S0294-1449(02)00022-7]
The cauchy problem for the schroedinger equation in dimension three with concentrated nonlinearity
Dell'Antonio, Gianfausto;Teta, Alessandro
2003
Abstract
We consider the Schrodinger equation in R-3 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 H-1-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
