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Homoclinic solutions for a class of the second order Hamiltonian systems. (English) Zbl 1080.37067
Summary: We study the existence of homoclinic orbits for the second-order Hamiltonian system q ¨+V q (t,q)=f(t), where q n and VC 1 (× n ,), and 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 infinity and f is sufficiently small in L 2 (, n ). A homoclinic orbit is obtained as a limit of 2kT-periodic solutions of a certain sequence of the second-order differential equations.

37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
58E05Abstract critical point theory
34C37Homoclinic and heteroclinic solutions of ODE
70H05Hamilton’s equations