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

In this paper, we are concerned with the Littlewood's boundedness problem and the existence of quasi-periodic solutions for the nonlinear differential equation of the motions of relativistic oscillators with anharmonic potentialsddt(x′1−|x′|2)+|x|α−1x=p(t), where the 1-periodic function p(t) is a smooth function and α is a positive constant.