Unboundedness in a Duffing Equation with Polynomial Potentials

In this paper, a continuous periodic function p(t) is constructed such that the Duffing equation d2x/dt2+x2n+1+p(t) xl=0 with p(t) C0 (S1), n 2, 2n+1>l n+2 possesses an unbounded solution, which shows that the smoothness of the coefficients of the perturbation does influence the boundedness of solutions.