Boundedness and Stability of Solutions to Certain Second Order Differential Equations
Автор(ы):
A. T. Ademola
Department of Mathematics,
Obafemi Awolowo University, Ile-Ife, Nigeria
atademola@oauife.edu.ng
Аннотация:
In this paper the behaviour of solutions
of certain second order nonlinear non-autonomous differential equations is considered.
By employing the Lyapunov's second method, a suitable complete Lyapunov function
is constructed and used to establish sufficient conditions that guarantee existence
of solutions that are periodic, uniformly asymptotically stable and uniformly ultimately bounded.
Obtained results are not only new but also include many outstanding recent results in the literature.
Ключевые слова
- nonlinear differential equation
- periodic solutions
- second order
- uniform stability
- uniform ultimate boundedness
Ссылки:
- Alaba, J. G., and Ogundare, B. S.; Asymptotic behaviour of solutions of certain second order non-autonomous nonlinear ordinary differential equation, International Journal of Pure and Applied Mathematics, vol. 90, no. 4, (2014), 467 - 483
- Grigoryan, G. A.; Boundedness and stability criteria for linear ordinary differential equations of the second order, Russian Mathematics (Iz. VUZ), } vol. 57, } no. 12, (2013), 8 - 15
- Kroopnick A. J.; Bounded solutions to x’’+q(t)b(x)=f(t), Int. J. Math. Edu. Sci. Tec. 41, 6, (2010), 829 - 836
- Ogundare, S. B., and Afuwape, A. U.; Boundedness and stability properties of solutions of generalized Lienard equation, Kochi J. Math., 9 (2014), 97 - 108
- Ogundare, S. B., and Okecha, G. E.; Boundedness, periodicity and stability of solution
+a(t)g(
)+b(t)h(x)=p(t; x, 
), Math. Sci. Res. J., vol. 11, no. 5, (2007), 432 - 443
- Tunc, C.; A note on boundedness of solutions to a class of non-autonomous differential equations of second order, Applicable Analysis and Discrete Mathematics, vol. 4, no. 2 (2010), 361 - 372
- Tunc, C.; A note on the bounded solutions, Appl. Math. Inf. Sci., vol. 8, no. 1, (2014), 393 - 399
- Tunc, C.; Boundedness analysis for certain two-dimensional differential systems via a Lyapunov approach, Bull. Math. Soc. Sci. Math. Roumanie (N. S. )} 53, (101), (2010), 61 - 68
- Tunc, C.; Boundedness results for solutions of certain nonlinear differential equations of the second order, Journal of the Indonesian Mathematical Society, vol. 16, no. 2, (2010), 115 - 126
- Yoshizawa, T.; Liapunov's function and boundedness of solutions, Funkcialaj Ekvacioj, 2, (1958), 71-103
- Yoshizawa, T.; Stability theory by Liapunov's second method, The Mathematical Society of Japan (1966)
- Yoshizawa, T.; Stability theory and existence of periodic solutions and almost periodic solutions, Spriger-Verlag, New York. Heidelberg. Berlin (1975)
