## 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.

### MSC:

 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 34B37 Boundary value problems with impulses for ordinary differential equations 47J30 Variational methods involving nonlinear operators
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### References:

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