Scattered homoclinics to a class of 
 time-recurrent Hamiltonian systems

Gregory S. Spradlin

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In this paper, we deal with the existence of periodic solutions of the $p (t)$ -Laplacian Hamiltonian system $\{\begin{matrix} \frac{d}{d t} (| \dot{u} (t) |^{p (t) - 2} \dot{u} (t)) = \nabla F (t, u (t)) a.e. t \in [0, T], \\ u (0) - u (T) = \dot{u} (0) - \dot{u} (T) = 0 . \end{matrix}$ Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.

On periodic solutions of non-autonomous second order Hamiltonian systems

Xingyong Zhang, Yinggao Zhou (2010)

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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.

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