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Multiple periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian and partially periodic potentials

  • Zhihua Hu , Qin Jiang , Sheng Ma and Daniel Paşca EMAIL logo
Published/Copyright: February 17, 2023
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Abstract

In this paper, multiple periodic solutions are obtained for second-order Hamiltonian systems with (q, p)-Laplacian when the nonlinearity is partially periodic. New results are deduced by using minimax principle via critical point theory.


The last author dedicates this paper to Professor Jaume Llibre on the occasion of his 70th birthday, with deep esteem and respect.


  1. (Communicated by Michal Fečkan)

References

[1] Liu, J. Q.: A generalized saddle point theorem, J. Differential Equations 82 (1989), 372–385.Search in Google Scholar

[2] Li, C.—Ou, Z. Q.—Tang, C. L.: Periodic solutions for non-autonomous second-order differential systems with (q, p)-Laplacian, Electron. J. Differential Equations 64 (2014), 1–13.Search in Google Scholar

[3] Mawhin, J.—Willem, M.: Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences, 74. Springer-Verlag, New York, 1989.Search in Google Scholar

[4] Paşca, D.—Tang, C. L.: Some existence results on periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian, Appl. Math. Lett. 23 (2010), 246–251.Search in Google Scholar

[5] Paşca, D.: Periodic solutions of a class of nonautonomous second order differential systems with (q, p)-Laplacian, Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 841–850.Search in Google Scholar

[6] Paşca, D.—Tang, C. L.: New existence results on periodic solutions of nonautonomous second order differential systems with (q, p)-Laplacian, Bull. Belg. Math. Soc. Simon Stevin 19 (2012), 19–27.Search in Google Scholar

[7] Paşca, D.—Wang, Z. Y.: New existence results on periodic solutions of nonautonomous second order Hamiltonian systems with (q, p)-Laplacian, Bull. Belg. Math. Soc. Simon Stevin 20 (2013), 155–166.Search in Google Scholar

[8] Paşca, D.—Wang, Z. Y.: On periodic solutions of nonautonomous second order Hamiltonian systems with (q, p)-Laplacian, Electron. J. Qual. Theory Differ. Equ. 106 (2016), 1–9.Search in Google Scholar

[9] Tang, C. L.—Wu, X. P.: A note on periodic solutions of nonautonomous second order systems, Proc. Amer. Math. Soc. 132(5) (2003), 1295–1303.Search in Google Scholar

[10] Wang, Z. Y.—Zhang, J. H.: Periodic solutions of a class of second order non-autonomous Hamiltonian systems, Nonlinear Anal. 72 (2010), 4480–4487.Search in Google Scholar

[11] Yang, X. X.—Chen, H. B.: Existence of periodic solutions for sublinear second order dynamical system with (q, p)-Laplacian, Math. Slovaca 63(4) (2013), 799–816.Search in Google Scholar

[12] Zhang, X.—Tang, X.: Periodic solutions for an ordinary p-Laplacian system, Taiwanese J. Math. 15 (2011), 1369–1396.Search in Google Scholar

Received: 2021-01-31
Accepted: 2021-12-05
Published Online: 2023-02-17
Published in Print: 2023-02-23

© 2023 Mathematical Institute Slovak Academy of Sciences

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