01-392 Adami R., Dell'Antonio G., Figari R., Teta A.

The Cauchy Problem for the Schroedinger Equation in Dimension Three with Concentrated Nonlinearity (66K, LATeX 2e) Oct 22, 01

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Abstract. We consider the Schroedinger 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.

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