Existence of second periodic solutions to ordinary differential systems (Q2766298)

The author studies \(2\pi\)-periodic solutions to some weakly coupled system of \(n\) ordinary differential equations with real parameters NEWLINE\[NEWLINE x''_i(t)+ g_i(t, x_i(t))+ h_i(t, x(t))= s_i,\tag{\(*\)}NEWLINE\]NEWLINE where with \(g_i: I\times \mathbb{R}\to \mathbb{R}\) and \(h_i: I\times \mathbb{R}^n\to \mathbb{R}\) are \(2\pi\)-periodic in the first variable and continuous for \(i= 1,\dots, n\) and \(s_i\in \mathbb{R}\).NEWLINENEWLINENEWLINEThe proofs are based on differential inequalities and coincidence degree via the method of upper and lower solutions.NEWLINENEWLINEFor the entire collection see [Zbl 0973.00042].