Mass-constrained ground states of the stationary NLSE on periodic metric graphs
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Publication:2330913
DOI10.1007/S00030-019-0576-4zbMath1428.35650arXiv1811.06798OpenAlexW2966858768MaRDI QIDQ2330913
Publication date: 23 October 2019
Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1811.06798
Variational inequalities (49J40) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)
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Cites Work
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- Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy
- Threshold phenomena and existence results for NLS ground states on metric graphs
- On the lack of bound states for certain NLS equations on metric graphs
- Constrained energy minimization and orbital stability for the NLS equation on a star graph
- NLS ground states on graphs
- NLS ground states on metric graphs with localized nonlinearities
- Negative energy ground states for the \(L^{2}\)-critical NLSE on metric graphs
- Bifurcations of standing localized waves on periodic graphs
- Existence of infinitely many stationary solutions of the \(L^{2}\)-subcritical and critical NLSE on compact metric graphs
- Variational properties and orbital stability of standing waves for NLS equation on a star graph
- Multiple positive bound states for the subcritical NLS equation on metric graphs
- Nonlinear Schrödinger equations on periodic metric graphs
- Variational and stability properties of constant solutions to the NLS equation on compact metric graphs
- Extremal properties of eigenvalues for a metric graph.
- Validity of the NLS approximation for periodic quantum graphs
- Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs
- \(L^2\)-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features
- Bound states of the NLS equation on metric graphs with localized nonlinearities
- On the structure of critical energy levels for the cubic focusing NLS on star graphs
- A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
- High-energy asymptotics of the spectrum of a periodic square lattice quantum graph
- Quantum transport in ladder-type networks: the role of nonlinearity, topology and spin
- Nonlinear dynamics on branched structures and networks
- Periodic quantum graphs from the Bethe–Sommerfeld perspective
- Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit
- Ground States of the L 2-Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph
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