An application of KAM theorem of reversible systems (Q1180003)

Consider the nonlinear differential equation \(\ddot x+bx\dot x+cx^{2n+1}=p(t)\), \(n\geq 2\), \(p\) is odd, \(2\pi\)-periodic and continuous; \(b\), \(c\) are positive constants. The paper proves that, under some hypotheses, every solution of this equation is bounded, and that, for every integer \(m\geq 1\), there are at least two periodic solutions having minimal period \(2m\pi\). The problem of the existence of a quasiperiodic solution is analyzed too.