Non-existence of Multi-peak Solutions to the Schrödinger-Newton System with L2-constraint

In this paper, we are concerned with the the Schrödinger-Newton system with L 2 -constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V ( x ) under certain assumptions on asymptotic behavior of V ( x ) and its first d...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 39; no. 4; pp. 868 - 877
Main Authors Guo, Qing, Duan, Li-xiu
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Asymptotic properties
Critical point
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Schrodinger equation
Theoretical
35J20
35J60
Non-existence
Schrödinger-Newton equation
Multi-peak solutions
Pohozaev identity
Normalized solutions
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Summary:In this paper, we are concerned with the the Schrödinger-Newton system with L 2 -constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V ( x ) under certain assumptions on asymptotic behavior of V ( x ) and its first derivatives near these points. Especially, the critical points of V ( x ) in this paper must be degenerate. The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-023-1086-z