An Asymptotic Result in Forced Oscillations of Pendulum-Type Equations

Abstract

**Please note that the full text is embargoed** ABSTRACT: The forced pendulum-type equation is given by [see pdf for notation] where [see pdf for notation] is continuous and T-periodic and p(t) is[see pdf for notation] -periodic. When g(x) = a sin x, a > 0, we obtain the classical pendulum equation. The question of existence of [see pdf for notation] periodic solution of (1.1) for a given p(t) has been studied recently in [1], [3], [5] (cf. [4] for an extensive bibliography). Throughout this paper we denote by [see pdf for notation] the average of [see pdf for notation]. Some of the existence literature obtains sufficient conditions on the magnitudes of [see pdf for notation] and [see pdf for notation] in order that (1.1) have [see pdf for notation]- periodic solutions. A second category of results in the literature involves studying the problem (1.1) as characterizing the p(t) that are in the range of the operator [see pdf for notation]acting on [see pdf for notation]- periodic functions.