00-298 Adami R., Teta A.
A Class of Nonlinear Schroedinger Equations with Concentrated Nonlinearity (66K, LaTeX) Jul 20, 00
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Abstract. We consider the nonlinear Schr\"{o}dinger 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 $H^{\rho}$ are given. We also prove the conservation of the $L^{2}$-norm and the energy of the solution and give a global existence result for repulsive and weakly attractive interaction in the space $H^{1}$. Finally we prove the existence of blow-up solutions for strongly attractive interaction.

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