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Infinitely many rotating periodic solutions for suplinear second-order impulsive Hamiltonian systems. (English) Zbl 1406.37047

Summary: This paper aims to investigate a class of second-order suplinear Hamiltonian systems generated by impulsive effects. By introducing a new energy functional and employing the Fountain theorem, the existence of infinitely many rotating periodic solutions is obtained.

MSC:

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34A37 Ordinary differential equations with impulses
Full Text: DOI

References:

[1] D’Onofrio, A., On pulse vaccination strategy in the SIR epidemic model with vertical transmission, Appl. Math. Lett., 18, 729-732 (2005) · Zbl 1064.92041
[2] Nenov, S., Impulsive controllability and optimization problems in population dynamics, Nonlinear Anal., 36, 881-890 (1999) · Zbl 0941.49021
[3] Du, Z.; Feng, Z., Periodic solutions of a neutral impulsive predator-prey model with Beddington-DeAngelis functional response with delays, J. Comput. Appl. Math., 258, 87-98 (2014) · Zbl 1330.37074
[4] Franco, D.; Nieto, J., Maximum principle for periodic impulsive first order problems, J. Comput. Appl. Math., 88, 149-159 (1998) · Zbl 0898.34010
[5] Agarwal, R.; O’Regan, D., Multiple nonnegative solutions for second order impulsive differential equations, Appl. Math. Comput., 114, 51-59 (2000) · Zbl 1047.34008
[6] Tian, Y.; Ge, W., Applications of variational methods to boundary value problem for impulsive differential equations, Proc. Edinb. Math. Soc., 51, 509-527 (2008) · Zbl 1163.34015
[7] Bai, L.; Dai, B., Three solutions for a \(p\)-Laplacian boundary value problem with impulsive effects, Appl. Math. Comput., 217, 9895-9904 (2011) · Zbl 1226.34029
[8] Nieto, J.; O’Regan, D., Variational approach to impulsive differential equations, Nonlinear Anal., 10, 680-690 (2009) · Zbl 1167.34318
[9] Sun, J.; Chen, H.; Nieto, J., Infinitely many solutions for second-order Hamiltonian system with impulsive effects, Math. Comput. Modelling, 54, 544-555 (2011) · Zbl 1225.37070
[10] Zhou, J.; Li, Y., Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects, Nonlinear Anal., 72, 1594-1603 (2010) · Zbl 1193.34057
[11] Zhang, Z.; Yuan, R., An application of variational methods to Dirichlet boundary value problem with impulses, Nonlinear Anal., 11, 155-162 (2010) · Zbl 1191.34039
[12] Chang, X.; Li, Y., Rotating periodic solutions of second order dissipative dynamical systems, Discrete Contin. Dyn. Syst. Ser. A, 36, 643-652 (2016) · Zbl 1332.34079
[13] Chang, X.; Li, Y., Rotating periodic solutions for second-orderdynamical systems with singularities ofrepulsive type, Math. Methods Appl. Sci., 40, 3092-3099 (2017) · Zbl 1373.34063
[14] Liu, G.; Li, Y.; Yang, Xue, Rotating periodic solutions for asymptotically linear second-order Hamiltonian systems with resonance at infinity, Math. Methods Appl. Sci., 40, 7139-7150 (2017) · Zbl 1387.34065
[15] Li, X.; Wu, X.; Wu, K., On a class of damped vibration problems with super-quadratic potentials, Nonlinear Anal., 72, 135-142 (2010) · Zbl 1186.34056
[16] Mawhin, J.; Willem, M., Critical Point Theory and Hamiltonian Systems (1989), Springer-Verlag: Springer-Verlag Berlin · Zbl 0676.58017
[17] Tang, X., New Super-quadratic conditions on ground state solutionsfor superlinear Schrödinger equation, Adv. Nonlinear Stud., 14, 361-373 (2014) · Zbl 1305.35036
[18] Bartsch, T., Infinitely many solutions of a symmetric Dirichlet problem, Nonlinear Anal., 20, 1205-1216 (1993) · Zbl 0799.35071
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