Periodic solutions for some nonautonomous second-order systems (Q1856925)

Some existence theorems are obtained for periodic solutions to second-order systems using the least action principle and minimax methods. The second-order system considered is of the form \[ \ddot u=\nabla F(t, u(t)),\quad u(0)- u(T)= 0,\qquad\dot u(0)-\dot u(T)= 0, \] where \(T> 0\) and \(F: [0,T]\times \mathbb{R}^N\to\mathbb{R}\) and \(F\) satisfies specified conditions.