Displaying similar documents to “Scattered homoclinics to a class of time-recurrent Hamiltonian systems”

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.

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.

Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3

Joanna Janczewska, Jakub Maksymiuk (2012)

Open Mathematics

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We consider a conservative second order Hamiltonian system q ¨ + ∇ V ( q ) = 0 in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.