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Bounded Palais-Smale sequences with Morse type information for some constrained functionals

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arxiv 2210.12626 v2 pith:Z2NY7Q5Q submitted 2022-10-23 math.AP

Jack Borthwick , Xiaojun Chang , Louis Jeanjean , Nicola Soave This is my paper · ORCID
classification math.AP
keywords boundedfunctionalsinformationmorsepalais-smalesequencestypecarrying
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In this paper, we study, for functionals having a mountain pass geometry on a constraint, the existence of bounded Palais-Smale sequences carrying Morse index type information.

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Cited by 2 Pith papers

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  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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