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

DOI10.1016/j.jde.2015.12.030zbMath1408.35206arXiv1506.05707OpenAlexW2209327664MaRDI QIDQ2634197

Yanyan Li

Publication date: 8 February 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.05707

zbMATH Keywords

nonlinear Schrödinger equationminimax methodsmetric graphslocalized nonlinearityKrasnosel'skii genus

Mathematics Subject Classification ID

Existence of solutions for minimax problems (49J35) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) NLS equations (nonlinear Schrödinger equations) (35Q55) Infinite-dimensional manifolds (46T05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (27)

Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs ⋮ Multiple positive bound states for the subcritical NLS equation on metric graphs ⋮ Standing waves on quantum graphs ⋮ On the lack of bound states for certain NLS equations on metric graphs ⋮ Doubly nonlinear Schrödinger ground states on metric graphs ⋮ Ground states of nonlinear Schrödinger equation on star metric graphs ⋮ Ground states for the NLS equation with combined local nonlinearities on noncompact metric 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 ⋮ Peaked and Low Action Solutions of NLS Equations on Graphs with Terminal Edges ⋮ Ground States of the L 2-Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph ⋮ On the nonlinear Dirac equation on noncompact metric graphs ⋮ Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit ⋮ Normalized solutions for the Kirchhoff equation on noncompact metric graphs ^* ⋮ Existence of infinitely many stationary solutions of the \(L^{2}\)-subcritical and critical NLSE on compact metric graphs ⋮ Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one ⋮ Variational and stability properties of constant solutions to the NLS equation on compact metric graphs ⋮ Uniqueness and non-uniqueness of prescribed mass NLS ground states on metric graphs ⋮ Quantum graphs and dimensional crossover: the honeycomb ⋮ One-dimensional versions of three-dimensional system: Ground states for the NLS on the spatial grid ⋮ Drift of Spectrally Stable Shifted States on Star Graphs ⋮ Edge-localized states on quantum graphs in the limit of large mass ⋮ NLS ground states on metric trees: existence results and open questions ⋮ An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity ⋮ Local minimizers in absence of ground states for the critical NLS energy on metric graphs ⋮ Existence of the ground state for the NLS with potential on graphs ⋮ Mass-constrained ground states of the stationary NLSE on periodic metric graphs

Cites Work

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