Boundedness of solutions of some nonlinear differential equations

摘要

In this paper, the boundedness of solutions for the nonlinear differential equations is studied,x′′+f(x,t)x′+g(x,t)=0,where f(x,t)=∑k=0mak(t)x2k+1, g(x,t)=∑j=0n−1bj(t)x2j+1, ak(t), bj(t) are continuous periodic functions with period 1, 0⩽k⩽m, 0⩽j⩽n−1. Moreover, 2m+2⩽n.