Homoclinic solutions for a class of the second order Hamiltonian systems
By M. Izydorek, Joanna Janczewska. 2005
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Abstract We study the existence of homoclinic orbits for the second order Hamiltonian system q ¨ + V q ( t , q ) = f ( t ) , where q ∈ R n and V ∈ C 1 ( R × R n , R ) , V ( t , q ) = - K ( t , q ) + W ( t , q ) is T-periodic in t. A map K satisfies the “pinching” condition b 1 | q | 2 ⩽ K ( t , q ) ⩽ b 2 | q | 2 , W is superlinear at the infinity and f is sufficiently small in L 2 ( R , R n ) . A homoclinic orbit is obtained as a limit of 2 kT -periodic solutions of a certain sequence of the second order differential equations.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/20c0a7854d5d51b7b0723dcf46a00c545817d950
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential (2009, background): “Here we only mention [1–15].”
- Existence and multiplicity of homoclinic solutions for a class of damped vibration problems (2011, unknown): “1), (for example, see [1–15]).”