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Keywords:
periodic solution; Hamiltonian system; $p(t)$-Laplacian system; critical point; minimax principle; least action principle
periodic solution; Hamiltonian system; $p(t)$-Laplacian system; critical point; minimax principle; least action principle
Summary:
In this paper, we deal with the existence of periodic solutions of the $p(t)$-Laplacian Hamiltonian system $$ \begin {cases} \dfrac {{\rm d}}{{\rm d}t}(|\dot {u}(t)|^{p(t)-2}\dot {u}(t)) =\nabla F(t,u(t))\quad \text {a.e.} \ t\in [0,T] ,\\ u(0)-u(T)=\dot {u}(0)-\dot {u}(T)=0. \end {cases} $$ 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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