A supercritical scalar field equation with a forcing term

Kazuhiro Ishige, Shinya Okabe, Tokushi Sato

Research output: Contribution to journalArticle

Abstract

This paper is concerned with the elliptic problem for a scalar field equation with a forcing term −Δu+u=up+κμ in RN, where N≥2, p>1, κ>0 and μ is a Radon measure in RN with a compact support. Under a suitable integrability condition on μ, we give a complete classification of the existence and nonexistence of positive solutions decaying at the space infinity in the case of 1<p<pJL. Here pJL is the so-called Joseph-Lundgren exponent.

Original languageEnglish
Pages (from-to)183-212
Number of pages30
JournalJournal des Mathematiques Pures et Appliquees
Volume128
DOIs
Publication statusPublished - 2019 Aug

Keywords

  • Scalar field equation
  • Supercritical
  • The Joseph-Lundgren exponent

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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