Multiplicity of radial and nonradial solutions to equations with fractional operators

Research output: Contribution to journalArticle

Abstract

In this paper, we study the existence of radial and nonradial solutions to the scalar field equations with fractional operators. For radial solutions, we prove the existence of infinitely many solutions under N ≥ 2. We also show the existence of least energy solution (with the Pohozaev identity) and its mountain pass characterization. For nonradial solutions, we prove the existence of at least one nonradial solution under N ≥ 4 and infinitely many nonradial solutions under either N = 4 or N ≥ 6. We treat both of the zero mass and the positive mass cases.

Original languageEnglish
Pages (from-to)3501-3530
Number of pages30
JournalCommunications on Pure and Applied Analysis
Volume19
Issue number7
DOIs
Publication statusPublished - 2020 Jul

Keywords

  • Nonradial solutions
  • Positive mass case
  • Radial solutions
  • Symmetric mountain pass thoerem
  • Zero mass case

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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