On the Boundedness of Solutions of a Non-autonomous Differential Equation of Second Order
DOI:
https://doi.org/10.5644/SJM.07.1.03Keywords:
Non-autonomous, differential equation, second order, boundednessAbstract
We study the boundedness of the solutions to a non-autonomous differential equation of second order. With this work, we improve some stability results in the literature of boundedness of the solutions. We give two examples to illustrate the theoretical analysis in this work.
2000 Mathematics Subject Classification. 34C11, 34D20
Downloads
References
S. Ahmad and M. Rama Mohana Rao, Theory of Ordinary Differential Equations. With Applications in Biology and Engineering, Affiliated East-West Press Pvt. Ltd., New Delhi, 1999.
John W. Baker, Stability properties of a second order damped and forced nonlinear differential equation, SIAM J. Appl. Math., 27 (1974), 159–166.
C. Cheng and J. Xu, Boundedness of solutions for a class of second-order differential equations, Nonlinear Anal., 68 (7) (2008), 1993–2004.
J. Kato, On a boundedness condition for solutions of a generalized Li ´enard equation, J. Differ. Equations, 65 (2) (1986), 269–286.
J. Kato, A simple boundedness theorem for a Li´enard equation with damping, Ann. Pol. Math., 51 (1990), 183–188.
I. A. Malyseva, Boundedness of solutions of a Li´enard differential equation, Differ. Uravn., 15 (8) (1979), 1420–1426
M. Mure¸san, Boundedness of solutions for Li´enard type equations, Mathematica, 40(63) (2) (1998), 243–257.
Juan E. N´apoles Vald´es, Boundedness and global asymptotic stability of the forced Li´enard equation (Spanish), Rev. Union Mat. Argent., 41 (4) (2000), 47–59.
S. H. Saker, Boundedness of solutions of second-order forced nonlinear dynamic equations, Rocky Mt. J. Math., 36 (6) (2006), 2027–2039.
C. Tunç Some new stability and boundedness results on the solutions of the nonlinear vector differential equations of second order, Iran. J. Sci. Technol. Trans. A Sci., 30 (2) (2006), 213–221.
C. Tun¸c, A new boundedness theorem for a class of second order differential equations, Arab. J. Sci. Eng. Sect. A Sci., 33 (1) (2008), 83–92.
C. Tun¸c, Boundedness analysis for certain two-dimensional differential systems via a Lyapunov approach, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 53(101) (1) (2010), 1–8.
C. Tun¸c, A note on boundedness of solutions to a class of non-autonomous differential equations of second order, Appl. Anal. Discrete Math., 4 (2010), 361–372.
C. Tun¸c, and E. Tun¸c, On the asymptotic behavior of solutions of certain second-order differential equations, J. Franklin Inst., 344 (5) (2007), 391–398.
L. Zhao, Boundedness and convergence for the non-Li´enard type differential equation, Acta Math. Sci. Ser. B Eng. Ed., 27 (2) (2007), 338–346.
L. Wang, Boundedness of nonlinear second order differential equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16 (2009), Differential Equations and Dynamical Systems, suppl. S1, 88–93.
