Local minimizers in absence of ground states for the critical NLS energy on metric graphs

DOI10.1017/prm.2020.36zbMath1464.35329arXiv1909.11533OpenAlexW3028286876MaRDI QIDQ4987474

Dario Pierotti, Nicola Soave, Gianmaria Verzini

Publication date: 3 May 2021

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.11533

zbMATH Keywords

normalized solutionsnon-linear Schrödinger equationnon-compact metric graphs\(L^2\)-critical exponent

Mathematics Subject Classification ID

Variational inequalities (49J40) Critical exponents in context of PDEs (35B33) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

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