Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit
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Publication:4631726
DOI10.1137/18M1211714zbMath1411.35263arXiv1807.06937MaRDI QIDQ4631726
Raffaele Carlone, Lorenzo Tentarelli, William Borrelli
Publication date: 18 April 2019
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1807.06937
Existence of solutions for minimax problems (49J35) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Time-dependent Schrödinger equations and Dirac equations (35Q41) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)
Related Items (21)
Exact Number of Positive Solutions for the Kirchhoff Equation ⋮ Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs ⋮ Standing waves on quantum graphs ⋮ Doubly nonlinear Schrödinger ground states on metric graphs ⋮ Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover ⋮ Spectral stability and instability of solitary waves of the Dirac equation with concentrated nonlinearity ⋮ Nonrelativistic limit and nonexistence of stationary solutions of nonlinear Dirac equations ⋮ \(L^2\)-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features ⋮ D^²=H+¼ with point interactions ⋮ 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 ⋮ Normalized solutions for the Kirchhoff equation on noncompact metric graphs * ⋮ Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one ⋮ Unnamed Item ⋮ Quantum graphs and dimensional crossover: the honeycomb ⋮ Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations ⋮ 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 ⋮ Mass-constrained ground states of the stationary NLSE on periodic metric graphs ⋮ Spectral properties of relativistic quantum waveguides
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