Displaying similar documents to “Periodic solutions for second order Hamiltonian systems”

Impulsive boundary value problems for p ( t ) -Laplacian’s via critical point theory

Marek Galewski, Donal O'Regan (2012)

Czechoslovak Mathematical Journal

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In this paper we investigate the existence of solutions to impulsive problems with a p ( t ) -Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order...

On periodic solutions of non-autonomous second order Hamiltonian systems

Xingyong Zhang, Yinggao Zhou (2010)

Applications of Mathematics

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The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system 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 the least action principle.

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

Liang Zhang, X. H. Tang (2013)

Applications of Mathematics

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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.