Periodic solutions for some nonautonomous second-order systems. (English) Zbl 1024.34036

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.
Reviewer: P.Smith (Keele)


34C25 Periodic solutions to ordinary differential equations
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