Multiplicity of normalized semi-classical states for a class of nonlinear Choquard equations

This article is concerned with the existence of multiple normalized solutions for a class of Choquard equations with a parametric perturbation where is a constant, is a parameter, , , is unknown and appears as a Lagrange multiplier, is a continuous function with -subcritical growth, and is a continu...

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Bibliographic Details
Published in:Advances in nonlinear analysis 2024-09, Vol.13 (1), p.1-17
Main Authors: Wu, Jinxia, He, Xiaoming
Format: Article
Language:English
Subjects:
35A15
35B33
35J20
35J60
Choquard equations
Lusternik-Schnirelmann category
normalized solutions
variational methods
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Summary:This article is concerned with the existence of multiple normalized solutions for a class of Choquard equations with a parametric perturbation where is a constant, is a parameter, , , is unknown and appears as a Lagrange multiplier, is a continuous function with -subcritical growth, and is a continuous function, satisfying del Pino and Felmer’s local conditions. With the help of the penalization method, and Lusternik-Schnirelmann theory, we investigate the relationship between the number of positive normalized solutions and the topology of the set, where the potential attains its minimum value if the parameter is small.
ISSN:2191-950X
2191-950X
DOI:10.1515/anona-2024-0038