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), 477-500 [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.
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