Geodesic
Existence of Periodic Solutions of $p(t)$-Laplacian Systems
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 1
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In this paper, by using the least action principle in critical point theory, we obtain some existence theorems of periodic solutions for $p(t)$-Laplacian system \begin{equation*} \left\{ \begin{aligned} \frac{d}{dt}(|\dot{u}(t)|^{p(t)-2}\dot{u}(t))=\nabla F(t,u(t))\quad \text{a.e. }t\in[0,T] \\ (0)-u(T)=\dot{u}(0)-\dot{u}(T)=0, \end{aligned} \right. \end{equation*} which generalize some existence theorems.
Classification : 34C25, 35A15. 
@article{BMMS_2012_35_1_a2,
     author = {Liang Zhang and Yi Chen},
     title = {Existence of {Periodic} {Solutions} of $p(t)${-Laplacian} {Systems}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_1_a2/}
}
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Liang Zhang; Yi Chen. Existence of Periodic Solutions of $p(t)$-Laplacian Systems. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2012_35_1_a2/