On Littlewood’s boundedness problem for sublinear Duffing equations

Abstract

In this paper, we are concerned with the boundedness ofall the solutions and the existence of quasi-periodicsolutions for second order differential equationsx" g(x) =e(t),where the 1-periodic function e(t) is a smoothfunction and g(x) satisfies sublinearity:sign(x) . g(x) -->+infinity, g(x)/x --> 0 as \x\ --> +infinity.