A priori bounds for periodic solutions of a Duffing equation
Consider the scalar differential equation \[ x''+ cx'+ g(x)= p(t),\quad t\in\mathbb{R},\tag{\(*\)} \] where \(p\) is continuous, \(2\pi\)-periodic and with zero mean. By establishing a priori bounds for \(2\pi\)-periodic solutions of the auxiliary equation \[ x''+\lambda cx'+\lambda g(x)=\lambda p(t),\quad t\in\mathbb{R},\;\lambda\in (0,1) \] the authors prove under relatively simple conditions on \(c\), \(g\), \(p\) the existence of \(2\pi\)-periodic solutions of \((*)\) by using the coincidence degree.
scientific article; zbMATH DE number 5354619