Boundedness of solutions to superlinear reversible systems (Q5933943)

Here, the author studies the boundedness of solutions for the following differential equation \[ \ddot x + f(x,t)\dot x + g(x,yt) = 0, \] where the functions \(f\) and \(g\) are \(1\)-periodic in \(t\). Based on KAM theorem for reversible systems and the techniques and ideas developed by \textit{M. Levi} [Commun. Math. Phys. 143, No. 1, 43-83 (1991; Zbl 0744.34043)] and \textit{B. Liu} [Sci. China, Ser. A 34, No. 9, 1068-1078 (1991; Zbl 0742.34032)], he proves that under some suitable conditions on \(f\) and \(g\) all solutions are bounded and there are many quasiperiodic solutions.