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Homoclinic orbits for superquadratic Hamiltonian systems with small forcing terms. (English) Zbl 1217.34073

Summary: We prove the existence of homoclinic orbits for the second order Hamiltonian system:

q ¨(t)+V(t,q(t))=f(t),

where VC 1 (× n ,), V(t,q)=-K(t,q)+W(t,q) is T-periodic in t, K satisfies the “pinching” condition b 1 |q| 2 K(t,q)b 2 |q| 2 and W is superquadratic at infinity and needs not satisfy the global Ambrosetti-Rabinowitz condition. A homoclinic orbit is obtained as the limit of 2kT-periodic solutions of a certain sequence of second order differential equations.

34C37Homoclinic and heteroclinic solutions of ODE
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
34C25Periodic solutions of ODE