Geodesic
Periodic solutions for some nonautonomous $p(t)$-Laplacian Hamiltonian systems
Applications of Mathematics, Tome 58 (2013) no. 1, pp. 39-61 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     author = {Zhang, Liang and Tang, X. H.},
     title = {Periodic solutions for some nonautonomous $p(t)${-Laplacian} {Hamiltonian} systems},
     journal = {Applications of Mathematics},
     pages = {39--61},
     year = {2013},
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     doi = {10.1007/s10492-013-0002-x},
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     zbl = {1274.34129},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0002-x/}
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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

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