Cite

[1] R. Benterki and J. Llibre, Periodic solutions of the Duffing differential equation revisited via the averaging theory, J. of Nonlinear Modeling and Analysis 1 (2019), 10–26.Search in Google Scholar

[2] R. Benterki and J. Llibre, Periodic solutions of a class of Duffing differential equations, to appear in J. of Nonlinear Modeling and Analysis.Search in Google Scholar

[3] A. Buica, J.P. Françoise and J. Llibre, Periodic solutions of nonlinear periodic differential systems with a small parameter, Comm. Pure and Appl. Anal. 6 (2007), 103–111.10.3934/cpaa.2007.6.103Search in Google Scholar

[4] H.B. Chen and Y. Li, Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities, Proc. Amer. Math. Soc. 135 (2007), 3925–3932.10.1090/S0002-9939-07-09024-7Search in Google Scholar

[5] H. Chen and Y. Li, Rate of decay of stable periodic solutions of Duffing equations, J. Differential Equations 236 (2007), 493–503.10.1016/j.jde.2007.01.023Search in Google Scholar

[6] H. Chen and Y. Li, Bifurcation and stability of periodic solutions of Duffing equations, Nonlinearity 21 (2008), 2485–2503.10.1088/0951-7715/21/11/001Search in Google Scholar

[7] A. C. Lazer and P. J. Mckenna, On the existence of stable periodic solutions of differential equations of Duffing type, Proc. Amer. Math. Soc. 110 (1990), 125–133.10.1090/S0002-9939-1990-1013974-9Search in Google Scholar

[8] S. Liang, Exact multiplicity and stability of periodic solutions for a Duffing equation, Mediterr. J. Math. 10 (2013), 189–199.10.1007/s00009-012-0189-1Search in Google Scholar

[9] J. Llibre and A. Makhlouf, Periodic solutions for periodic second-order differential equations with variable potentials, J Appl. Anal. 24 (2018), 127–137,10.1515/jaa-2018-0013Search in Google Scholar

[10] J. Llibre and L. Roberto, On the periodic solutions of a class of Duffing differential equations, Discrete Contin. Dyn. Syst. 33 (2013), 277–282.10.3934/dcds.2013.33.277Search in Google Scholar

[11] I.G. Malkin, Some Problems of the theory of nonlinear oscillations, Gosudarstv. Izdat. Tehn-Teor. Lit. Moscow, 1956 (in Russian).Search in Google Scholar

[12] J. Mawhin, Seventy-five years of global analysis around the forcedpendulum equation, in Equadiff, Brno. Proceedings, Brno: Masaryk University 9 (1997), 115–145.Search in Google Scholar

[13] F.I. Njoku and P. Omari, Stability properties of periodic solutions of a Duffing equation in the presence of lower and upper solutions, Appl. Math. Comput 135 (2003), 471–490.10.1016/S0096-3003(02)00062-0Search in Google Scholar

[14] R. Ortega, Stability and index of periodic solutions of an equation of Duffing type, Boo. Uni. Mat. Ital B 3 (1989), 533–546.Search in Google Scholar

[15] M. Roseau, Vibrations non linéaires et théorie de la stabilité, (French) Springer Tracts in Natural Philosophy, Vol. 8 Springer-Verlag, Berlin-New York, 1966.Search in Google Scholar

[16] J.A. Sanders, F. Verhulst and J. Murdock, Averaging method in nonlinear dynamical systems, Appl. Math. Sci., Vol. 59, Springer, New York, 2007.Search in Google Scholar

[17] P.J. Torres, Existence and stability of periodic solutions of a Duffing equation by using a new maximum principale, Mediterr. J. Math. 1 (2004), 479–486.10.1007/s00009-004-0025-3Search in Google Scholar

[18] F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer, New York, 1996.10.1007/978-3-642-61453-8Search in Google Scholar

[19] F. Wang and H. Zhu, Existence, uniqueness and stability of periodic solutions of a Duffing equation under periodic and anti-periodic eigenvalues conditions, Taiwanese J of Math. 19 (2015), 1457–1468.10.11650/tjm.19.2015.3992Search in Google Scholar

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