On the lack of bound states for certain NLS equations on metric graphs

Abstract

The purpose of this paper is to prove some results on the absence of bound states for certain nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearity. In particular, we show how the topological and metric properties of graphs affect the existence/nonexistence of bound states. This work completes the discussion initiated in [17, 18].

20 pages, 9 figures

References in corpus (1)

• Fast solitons on star graphs

Cited by in corpus (17)

• Standing waves on quantum graphs
• $L^2$-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features
• Normalized solutions of $L^2$-supercritical NLS equations on noncompact metric graphs with localized nonlinearities
• NLS ground states on metric trees: existence results and open questions
• Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs
• Nonlinear Dirac Equation On Graphs With Localized Nonlinearities: Bound States And Nonrelativistic Limit
• Edge-localized states on quantum graphs in the limit of large mass
• On the nonlinear Dirac equation on noncompact metric graphs
• Ground states of the $L^2$-critical NLS equation with localized nonlinearity on a tadpole graph
• A note on the Dirac operator with Kirchoff-type vertex conditions on noncompact metric graphs
• An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity
• Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one
• An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions
• Normalized solutions of one-dimensional defocusing NLS equations with nonlinear point interactions
• Multiple positive bound states for the subcritical NLS equation on metric graphs
• Existence of infinite stationary solutions of the $L^2$-subcritical and critical NLSE on compact metric graphs
• Variational and stability properties of constant solutions to the NLS equation on compact metric graphs