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Homoclinic orbits for superquadratic Hamiltonian systems without a periodicity assumption. (English) Zbl 1221.37115
Summary: We consider the second-order Hamiltonian system q ¨(t)+V(t,q(t))=f(t) where V(t,q)=-K(t,q)+W(t,q). Under suitable conditions on the growth of W and K, we establish the existence of a nontrivial homoclinic orbit without any assumption of periodicity on V. This homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil-boundary-value problems which are obtained by the minimax methods.

MSC:
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
34C37Homoclinic and heteroclinic solutions of ODE
70H05Hamilton’s equations
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