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Zbl 1225.37070
Sun, Juntao; Chen, Haibo; Nieto, Juan J.
Infinitely many solutions for second-order Hamiltonian system with impulsive effects. (English)
[J] Math. Comput. Modelling 54, No. 1-2, 544-555 (2011). ISSN 0895-7177

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 2000:: *37J45 Periodic, homoclinic and heteroclinic orbits, etc.
34B37 Boundary value problems with impulses
47J30 Variational methods

Keywords: Hamiltonian systems; impulsive effects; variational methods; critical points

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Zentralblatt MATH Berlin [Germany]