Bound states of the NLS equation on metric graphs with localized nonlinearities

Abstract

We investigate the existence of multiple bound states of prescribed mass for the nonlinear Schrödinger equation on a noncompact metric graph. The main feature is that the nonlinearity is localized only in a compact part of the graph. Our main result states that for every integer k, the equation possesses at least k solutions of prescribed mass, provided that the mass is large enough. These solutions arise as constrained critical points of the NLS energy functional. Estimates for the energy of the solutions are also established.

19 pages

References in corpus (3)

• NLS ground states on metric graphs with localized nonlinearities
• The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit
• Threshold phenomena and existence results for NLS ground states on graphs

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