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On the Ground State for the NLS Equation on a General Graph

  • Domenico FincoEmail author
Chapter
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Part of the Springer INdAM Series book series (SINDAMS, volume 18)

Abstract

We review some recent results on the existence of the ground state for a nonlinear Schrödinger equation (NLS) posed on a graph or network composed of a generic compact part to which a finite number of half-lines are attached. In particular we concentrate on the main theorem in Cacciapuoti et al. (Ground state and orbital stability for the NLS equation on a general starlike graph with potentials, preprint arXiv:1608.01506) which covers the most general setting and we compare it with similar results.

Keywords

Concentration-compactness techniques Quantum graphs Non-linear Schrödinger equation 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Facoltà di IngegneriaUniversità Telematica Internazionale UninettunoRomaItaly

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