References
- [1] R. B
enterki 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. - [2] R. B
enterki and J. Llibre , Periodic solutions of a class of Duffing differential equations, to appear in J. of Nonlinear Modeling and Analysis. - [3] A. B
uica , 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. - [4] H.B. C
hen and Y. Li , Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities, Proc. Amer. Math. Soc. 135 (2007), 3925–3932. - [5] H. C
hen and Y. Li , Rate of decay of stable periodic solutions of Duffing equations, J. Differential Equations 236 (2007), 493–503. - [6] H. C
hen and Y. Li , Bifurcation and stability of periodic solutions of Duffing equations, Nonlinearity 21 (2008), 2485–2503. - [7] A. C. L
azer 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. - [8] S. L
iang , Exact multiplicity and stability of periodic solutions for a Duffing equation, Mediterr. J. Math. 10 (2013), 189–199. - [9] J. L
libre and A. Makhlouf , Periodic solutions for periodic second-order differential equations with variable potentials, J Appl. Anal. 24 (2018), 127–137, - [10] J. L
libre and L. Roberto , On the periodic solutions of a class of Duffing differential equations, Discrete Contin. Dyn. Syst. 33 (2013), 277–282. - [11] I.G. M
alkin , Some Problems of the theory of nonlinear oscillations, Gosudarstv. Izdat. Tehn-Teor. Lit. Moscow, 1956 (in Russian). - [12] J. M
awhin , Seventy-five years of global analysis around the forcedpendulum equation, in Equadiff, Brno. Proceedings, Brno: Masaryk University 9 (1997), 115–145. - [13] F.I. N
joku 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. - [14] R. O
rtega , Stability and index of periodic solutions of an equation of Duffing type, Boo. Uni. Mat. Ital B 3 (1989), 533–546. - [15] M. R
oseau , Vibrations non linéaires et théorie de la stabilité, (French) Springer Tracts in Natural Philosophy, Vol. 8 Springer-Verlag, Berlin-New York, 1966. - [16] J.A. S
anders , F. Verhulst and J. Murdock , Averaging method in nonlinear dynamical systems, Appl. Math. Sci., Vol. 59, Springer, New York, 2007. - [17] P.J. T
orres , Existence and stability of periodic solutions of a Duffing equation by using a new maximum principale, Mediterr. J. Math. 1 (2004), 479–486. - [18] F. V
erhulst , Nonlinear Differential Equations and Dynamical Systems, Universitext, Springer, New York, 1996. - [19] F. W
ang 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.