A Class of Nonlinear Schrödinger Equations with Concentrated Nonlinearity

✍ Scribed by Riccardo Adami; Alessandro Teta

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 209 KB
• Volume: 180
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3697

✦ Synopsis

We consider the nonlinear Schro 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 \ 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.