Geodesic
Periodic solutions for some nonautonomous $p(t)$-Laplacian Hamiltonian systems
Applications of Mathematics, Tome 58 (2013) no. 1, pp. 39-61.

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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.
DOI : 10.1007/s10492-013-0002-x
Classification : 34C25, 37J45, 58E50
Keywords: periodic solution; Hamiltonian system; $p(t)$-Laplacian system; critical point; minimax principle; least action principle 
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     title = {Periodic solutions for some nonautonomous $p(t)${-Laplacian} {Hamiltonian} systems},
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Zhang, Liang; Tang, X. H. Periodic solutions for some nonautonomous $p(t)$-Laplacian Hamiltonian systems. Applications of Mathematics, Tome 58 (2013) no. 1, pp. 39-61. doi : 10.1007/s10492-013-0002-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0002-x/

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