Morse Indices of the Solutions to the Liouville-Gel'fand Problem with Variable Coefficients

• Sato Tomohiko

  Nihon University

• Suzuki Takashi

  Osaka University

Abstract

We consider a sequence of blow-up solutions to the Liouville-Gel'fand problem with variable coefficients, and their linearized eigenvalue problems. We show the precise coincidence of the Morse indices of the solution and the critical point of the Hamiltonian of the singular limit. The results are natural extensions of those for constant coefficients.

Journal

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 61 (2), 229-265, 2018

  Division of Functional Equations, The Mathematical Society of Japan

Keywords

• Liouville-Gel'fand problem
• Point vortex
• Hamiltonian
• Morse index

Details

• CRID: 1390282763019134976
• NII Article ID: 130007411716
• DOI: 10.1619/fesi.61.229
• ISSN: 05328721
• Web Site: https://www.jstage.jst.go.jp/article/fesi/61/2/61_229/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed