Boundedness of solutions of Duffing's equation

AbstractJ. Littlewood, L. Markus, and J. Moser proposed independently the boundedness problem for solutions of Duffing's equation: x + g(x) = p(t), where p(t) is continuous and periodic and g(x) is superlinear at infinity. The purpose of this paper is to prove that all solutions of the above-mentioned Duffing's equation are bounded for t ∈ R when p(t) is even (or when p(t) is odd and g(x) is odd)