Global uniqueness of homoclinic orbits for a class of fourth order equations

C. J. Amick, J. F. Toland

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In this paper we show the global existence and uniqueness of certain orbits homoclinic to the zero stationary solution of the fourth order equation {Mathematical expression} when α, γ>0>β, dk/dx<0 for x>0 and K(0)=0. The existence problem is approached via the general theory of [1] and uniqueness follows from the Maximum Principle and some geometrical observations about the role of convexity. There are no small amplitude assumptions.

Original languageEnglish
Pages (from-to)591-597
Number of pages7
JournalZAMP Zeitschrift für angewandte Mathematik und Physik
Issue number4
Publication statusPublished - 1 Jul 1992

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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