Littlewood's problem for isochronous oscillators (Q1040661)

The authors deal with the boundedness of solutions of isochronous oscillators \[ x''+V'(x)=p(t),\tag{*} \] where \(p\) is \(T\)-periodic and \(V\) is a \(T\)-isochronous potential, meaning that all nontrivial solutions of \(x''+V'(x)=0\) are periodic, with minimal period \(T\). By exchanging the role of time variable and angular variable and using ``small twist theorem'', the authors prove that, if \(\Phi(t)=\int_0^Tp(t)\psi(t+\theta)dt\) is of constant sign, then all solutions of (*) are bounded.