On Littlewood's boundedness problem for relativistic oscillators with singular potentials

In this paper, we study the following nonlinear differential equations of motions of relativistic oscillators with singular potentialsddt(x′1−(x′)2)+V′(x)=p(t), where V is a singular potential and p is a 1-periodic function. We will prove the boundedness of all solutions and the existence of infinitely many quasi-periodic solutions via Moser's twist theorem.