Multiple periodic solutions to a class of second-order nonlinear mixed-type functional differential equations.

Shu, Xiao-Bao; Xu, Yuan-Tong

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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.

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