Unboundedness in a Duffing equation with polynomial potentials (Q1968706)

In this paper, it is proved that there exists a periodic function \(p(t)\) such that the Duffing equation \(d^2x/dt^2+x^{2n+1}+p(t)x^{2n}=0\), with \(n\geq 2\), possesses a solution which escapes to infinity in finite time.