Subharmonic solutions for second order differential systems (Q1910056)

The existence of subharmonic solutions of the system \(u_{tt}+ G' (u)= f(t)\) where \(f: \mathbb{R}\to \mathbb{R}^+\) is periodic with minimal period \(T>0\). A sequence \(\{u_{k_i}\}\) of solutions are sought where \(u_{k_i}\) is a periodic function with minimal period \(k_i T\) and \(k_i\to \infty\) as \(i\to \infty\). The proof uses the Morse index theorem.