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Homoclinic solutions for a class of the second-order impulsive Hamiltonian systems. (English) Zbl 1296.34121

Summary: This paper is concerned with the existence of homoclinic solutions for a class of the second order impulsive Hamiltonian systems. By employing the Mountain Pass Theorem, we demonstrate that the limit of a \(2kT\)-periodic approximation solution is a homoclinic solution of our problem.

MSC:

34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34A37 Ordinary differential equations with impulses
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
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