The Lagrangian stability for a class of second-order quasi-periodic reversible systems
Summary: We study the following second-order differential equation \[ (\Phi_p(x'))' + f(x, t) \Phi_p(x') + g(x, t) = 0, \] where \(\Phi_p(s) = |s|^{(p-2)} s\), \(p > 0\). \(f(x, t)\) and \(g(x, t)\) are real analytic functions in \(x\) and \(t\), \(2a\pi_p\)-periodic in \(x\), and quasi-periodic in \(t\) with frequencies \((\omega_1, \dots, \omega_m)\). Under some odd-even property of \(f(x, t)\) and \(g(x, t)\), we obtain the existence of invariant curves for above equation by a variant of the small twist theorem. Then, all solutions for the above equation are bounded in the sense of \(\text{sup}_{t \in\mathbb R}|x'(t)| < + \infty\).
scientific article; zbMATH DE number 5997800