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Existence of homoclinic solutions for a class of second-order Hamiltonian systems with general potentials. (English) Zbl 1239.34046
Summary: Under some local conditions on \(W(t,u)\), the existence of homoclinic solutions is obtained for the nonperiodic second-order Hamiltonian systems \(u''(t)-L(t)u(t)+\nabla W(t,u(t)=f(t)\) as a limit of periodic solutions of a certain sequence of boundary-value problems which are obtained by a new critical point theorem.

MSC:
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37C29 Homoclinic and heteroclinic orbits for dynamical systems
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