Ground states of the $L^2$-critical NLS equation with localized nonlinearity on a tadpole graph

Abstract

The paper aims at giving a first insight on the existence/nonexistence of ground states for the $L^2$-critical NLS equation on metric graphs with localized nonlinearity. In particular, we focus on the tadpole graph, which, albeit being a toy model, allows to point out some specific features of the problem, whose understanding will be useful for future investigations.

12 pages, 5 figures. Keywords: minimization, metric graphs, critical growth, nonlinear Schrödinger equation, localized nonlinearity

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Cited by in corpus (7)

• 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
• On the nonlinear Dirac equation on noncompact metric graphs
• A note on the Dirac operator with Kirchoff-type vertex conditions on noncompact metric graphs
• Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one
• An existence theory for nonlinear equations on metric graphs via energy methods
• Variational and stability properties of constant solutions to the NLS equation on compact metric graphs