Adami R., Teta A.
A Class of Nonlinear Schroedinger Equations with Concentrated Nonlinearity
(66K, LaTeX)

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.