On the stability of the equilibrium position of an oscillator under periodic perturbations (Q2342049)

Consider the differential equation \[ \ddot x+ x^{p/q}= X(x,\dot x,t)\tag{\(*\)} \] under the assumptions (i) \(p\) and \(q\) are positive odd numbers with \(p>q\) and \(p/q\) irreducible. (ii) \(X:\mathbb{R}\times \mathbb{R}\times \mathbb{R}\to\mathbb{R}\) is real analytic in the first two variables, continuous and periodic in \(t\). (iii) The expansion of \(X\) in the first two variables does not contain terms of order less than \(p+1\). By means of some generalized polar coordinates the author derives conditions guaranteeing that the zero solution of \((*)\) is asymptotically stable.