High energy rotation type solutions of the forced pendulum equation

Patricio Felmer, André De Laire, Salomé Martínez, Kazunaga Tanaka

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this article we study the existence and asymptotic profiles of high-energy rotation type solutions of the singularly perturbed forced pendulum equation ε2u'ε+sin uε= ε in (-L, L). We prove that the asymptotic profile of these solutions is described in terms of an energy function which satisfy an integro-differential equation. Also we show that given a suitable energy function E satisfying the integro-differential equation, a family of solutions of the pendulum equation above exists having E as the asymptotic profile, when ε → 0.

Original languageEnglish
Pages (from-to)1473-1499
Number of pages27
JournalNonlinearity
Volume26
Issue number5
DOIs
Publication statusPublished - 2013 May 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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