A variational approach for standing waves of FitzHugh-Nagumo type systems

Chao Nien Chen, Kazunaga Tanaka

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We study the existence of radially symmetric solutions of FitzHugh-Nagumo type elliptic systems in RN (N≥2): -δu=g(u)-vin RN,-dδv+γv=uin RN,(u(x),v(x))→(0,0)as |x|→∞. We utilize a truncation technique and apply minimax arguments to the corresponding strongly indefinite functionalIγ(u,v)=12RN|∇ ;u|2-d|∇ ;v|2dx-RNG(u)+γ2v2-uvdx, defined on Hr1(RN)×Hr1(RN), to find positive and possibly sign-changing solutions of (*). In particular, we overcome difficulty related to Palais-Smale condition via our new scaling argument. When g(ξ)=ξ(1-ξ)(ξ-α), α∈(0,12), we improve the existence result of Reinecke-Sweers [23].

Original languageEnglish
Pages (from-to)109-144
Number of pages36
JournalJournal of Differential Equations
Volume257
Issue number1
DOIs
Publication statusPublished - 2014 Jul 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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