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Abstract
The purpose of this paper is to study the existence and multiplicity of periodic solution for the following non-autonomous second-order systems: u ¨ ( t ) = ∇ F ( t , u ( t ) ) a . e . t ∈ [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 . Some new existence and multiplicity theorems are obtained by using the least action principle and the minimax method.
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