Abstract
In this paper, we study the existence of periodic solutions of some non-autonomous second order Hamiltonian systems { u ̈ ( t ) = ∇ F ( t , u ( t ) ) , a.e. t ∈ [ 0 , T ] , u ( 0 ) − u ( T ) = u ̇ ( 0 ) − u ̇ ( T ) = 0 . We obtain some new existence theorems by the least action principle.
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