Duality in the optimal control for damped hyperbolic systems with positive control.

Lee, Mi Jin; Park, Jong Yeoul; Kwon, Young Chel

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On periodic solutions of non-autonomous second order Hamiltonian systems

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The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system $\{\begin{matrix} \ddot{u} (t) = \nabla F (t, u (t)), a.e. t \in [0, T], \\ u (0) - u (T) = \dot{u} (0) - \dot{u} (T) = 0 . \end{matrix}$ Some new existence theorems are obtained by the least action principle.