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Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs

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arxiv 2204.01043 v2 pith:ZARU6RZN submitted 2022-04-03 math.AP

Xiaojun Chang , Louis Jeanjean , Nicola Soave This is my paper · ORCID
classification math.AP
keywords boundcompactgraphsmassmetricprescribedstatesupon
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This paper is devoted to the existence of non-trivial bound states of prescribed mass for the mass-supercritical nonlinear Schr\"odinger equation on compact metric graphs. The investigation is based upon a general variational principle which combines the monotonicity trick and a min-max theorem with second order information, and upon the blow-up analysis of bound states with prescribed mass and bounded Morse index.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Normalized solutions on large smooth domains to the Schr\"{o}dinger equations with potential and combined nonlinearities: The Sobolev critical case

    math.AP 2024-12 reject novelty 6.0 of 10

    A variational existence proof for normalized critical NLS solutions on large domains contains a false Liouville step and sign errors, so the main theorems are not established.

  2. Normalized Solutions on large smooth domains to the Schr\"{o}dinger equation with potential and general nonlinearity: Mass super-critical case

    math.AP 2025-01 conditional novelty 4.0 of 10

    For mass-supercritical nonlinearities with an external potential, positive normalized solutions exist on sufficiently large star-shaped domains and, under a radial condition on the potential, in R^N.

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