Boundedness of solutions for semilinear duffing equations

摘要

In this paper, we are concerned with the boundedness of all the solutions for the semilinear Duffing equationx″+n2x+f(x)=p(t),where p(t) is a smooth 2π periodic function and the perturbation f(x) is bounded. Moreover the well-known Lazer–Leach condition is not satisfied.