New type of solutions for the nonlinear Schrödinger equation in RN

Lipeng Duan, Monica Musso

Research output: Contribution to journalArticlepeer-review

8 Citations (SciVal)

Abstract

We construct a new family of entire solutions for the nonlinear Schrödinger equation {−Δu+V(y)u=u p,u>0,inR N,u∈H 1(R N), where [Formula presented] and N≥3, and V(y)=V(|y|) is a positive bounded radial potential satisfying [Formula presented] for some fixed constants V 0,a,σ>0, and [Formula presented].

Original languageEnglish
Pages (from-to)479-504
Number of pages26
JournalJournal of Differential Equations
Volume336
Early online date28 Jul 2022
DOIs
Publication statusPublished - 5 Nov 2022

Bibliographical note

Funding Information:
L. Duan was supported by the China Scholarship Council and NSFC grants (No. 11771167 ). M. Musso has been supported by EPSRC research Grant EP/T008458/1 . Part of this paper was completed during the visit of L. Duan to M. Musso at the University of Bath. L. Duan would like to thank the Department of Mathematical Sciences for its warm hospitality and supports.

Funding Information:
L. Duan was supported by the China Scholarship Council and NSFC grants (No. 11771167). M. Musso has been supported by EPSRC research Grant EP/T008458/1. Part of this paper was completed during the visit of L. Duan to M. Musso at the University of Bath. L. Duan would like to thank the Department of Mathematical Sciences for its warm hospitality and supports.

Publisher Copyright:
© 2022 The Author(s)

Keywords

  • Finite Lyapunov-Schmidt reduction
  • Infinitely many solutions
  • New solutions
  • Nonlinear Schrödinger equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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