High energy rotation type solutions of the forced pendulum equation

Patricio Felmer, André de Laire, Salomé Martínez, Kazunaga Tanaka
2013 Nonlinearity  
In this article we study the existence and asymptotic profiles of high-energy rotation type solutions of the singularly perturbed forced pendulum equation ε 2 u ε + sin u ε = ε 2 α(t)u 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
more » ... lum equation above exists having E as the asymptotic profile, when ε → 0. Mathematics Subject Classification: 34D15, 34B15, 35B25
doi:10.1088/0951-7715/26/5/1473 fatcat:dd5rbeqlvbge5lw4gwquv7d7um