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Infinitely many solutions for second-order Hamiltonian system with impulsive effects. (English) Zbl 1225.37070
Summary: We study the existence of infinitely many solutions for a class of second-order impulsive Hamiltonian systems. By using the variational methods, we give some new criteria to guarantee that the impulsive Hamiltonian systems have infinitely many solutions under the assumptions that the nonlinear term satisfies superquadratics, asymptotically quadratic and subquadratics, respectively. Finally, some examples are presented to illustrate our main results.
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
34B37Boundary value problems for ODE with impulses
47J30Variational methods (nonlinear operator equations)
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