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Homoclinic solutions for a class of nonperiodic and noneven second-order Hamiltonian systems. (English) Zbl 1246.37084

Summary: The existence of homoclinic solutions is obtained for second-order Hamiltonian systems \(-\ddot u(t) + L(t)u(t) = \nabla W(t, u(t)) - f(t)\), as the limit of the solutions of a sequence of nil-boundary-value problems which are obtained by the mountain pass theorem, when \(L(t)\) and \(W(t,x)\) are neither periodic nor even with respect to \(t\).

MSC:

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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