Time maps and existence of periodic solutions to second-order quasilinear differential equations (Q2755684)

The author considers the following second-order quasilinear differential equation NEWLINE\[NEWLINE(\varphi_p(x'))'+g(x)=p(t),NEWLINE\]NEWLINE where \(\varphi_p: \mathbb{R} \rightarrow \mathbb{R}\) is given by \(\varphi_p(u)=|u|^{p-2} u, p>1,\) \(g(x), p(t)\) are continuous functions on \(\mathbb{R}\) and \(p(t)\) is a \(T\)-periodic function. When \(p=2,\) the equation becomes the well-known Duffing equation. By using asymptotic properties of the time maps, the author obtains some sufficient conditions to ensure the existence of at least one \(T\)-periodic solution.