Boundedness of solutions and existence of invariant tori for a generalized pendulum type equation (Q1387444)

A generalized pendulum-type equation is considered \[ \left(\varphi_p(x')\right)'=Q_x(t,x) . \] Here, \(\varphi_p:\mathbb{R}\to \mathbb{R}\) is the generalized one-dimensional Laplacian \(\varphi_p(u)=| u|^{p-2}u\), \(p>1\), the ``prime'' is a differentiation with respect to \(t\), \(Q(t,x)\) is an 1-periodic function in \(t\) and \(x\). It is proved that every solution to this equation is bounded (Moser's conjecture). Furthermore it is shown that the equation possesses infinitely many invariant tori and the solutions situated on these tori are quasiperiodic solutions.