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

作　　者：Qing GUO Li-xiu DUAN 

机构地区：[1]College of Science,Minzu University of China,Beijing 100081,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第4期868-877,共10页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11771469);Qing Guo is supported by National Natural Science Foundation of China(No.11771469)。

摘　　要：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.

关 键 词：Schrödinger-Newton equation NON-EXISTENCE Multi-peak solutions Normalized solutions Pohozaev identity 

分 类 号：O175.29[理学—数学]