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Periodic solutions for some nonautonomous p ( t ) -Laplacian Hamiltonian systems

Liang ZhangX. H. Tang — 2013

Applications of Mathematics

In this paper, we deal with the existence of periodic solutions of the p ( t ) -Laplacian Hamiltonian system d d t ( | u ˙ ( t ) | p ( t ) - 2 u ˙ ( t ) ) = F ( t , u ( t ) ) a.e. t [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 . 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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