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

Chao Nien Chen, Kazunaga Tanaka

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    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

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    ASJC Scopus subject areas

    • Analysis

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