High energy rotation type solutions of the forced pendulum equation

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 = ε2α(t)uε 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. Mathematics Subject Classification: 34D15, 34B15, 35B25 (Some figures may appear in colour only in the online journal)