A Note On Deformation Argument For L2 Normalized Solutions Of Nonlinear Schrödinger Equations And Systems

Norihisa Ikoma, Kazunaga Tanaka

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

Abstract. We study the existence of L2 normalized solutions for nonlinear Schrödinger equations and systems. Under new Palais-Smale type conditions, we develop new deformation arguments for the constrained functional on (Formula Presented). As applications, we give other proofs to the results of [5, 8, 22]. As to the results of [5, 22], our deformation result enables us to apply the genus theory directly to the corresponding functional to obtain infinitely many solutions. As to the result [8], via our deformation result, we can show the existence of vector solution without using constraint related to the Pohozaev identity.

Original languageEnglish
Pages (from-to)609-646
Number of pages38
JournalAdvances in Differential Equations
Volume24
Issue number11-12
Publication statusPublished - 2019 Nov

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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