(Differencialnie Uravnenia i Protsesy Upravlenia)

About
History
Editorial Page
Addresses
Scope
Editorial Staff
Submission Review
For Authors
Publication Ethics
Issues
Русская версия

**A. Adeyanju Adetunji**

Department of Mathematics,

Federal University of Agriculture,

Abeokuta, Nigeria.

In this paper, we employ a complete Lyapunov function, Demidovic theorem and the generalized theorems of Ezeilo to establish sufficient conditions for the existence of a limiting regime in the sense of Demidovic for certain second order nonlinear vector differential equation. We equally prove that the limiting regime is periodic or almost periodic with respect to variable t, uniformly in X, Y whenever the forcing term is periodic or almost periodic. The results in this paper are quiet new with respect to second order differential equations.

- convergence
- limiting regime
- Lyapunov function
- second order nonlinear differential equation
- uniformly periodic (or almost periodic) solution

- A. T. Ademola,
*Boundedness and stability of solutions to certain second order differential equations.*Differential Equations and Control Processes no. 3, Volume 2015 - A. T. Ademola, P. O. Arawomo, and A. S. Idowu,
*Stability, Boundedness and Periodic Solutions to Certain Second Order Delay Differential Equations.*Proyecciones Journal of Mathematics vol. 36, No. 2, pp. 257-282, June 2017. Universidad Catolica del Norte Antofagasta - Chile - A. T. Ademola, ~ B. S. Ogundare, ~ M. O. Ogundiran, and O. A. Adesina,
*Periodicity, stability and boundedness of solutions to a certain second order delay differential equations.*International Journal of Differential Equations, vol. 2016, Article ID 2843709, 10 pages, 2016 - O. A. Adesina and A. S. Ukpera,
*On the existence of a limiting regime in the sense of Demidovic for a certain fifth order nonlinear differential equation.*Mathematical Analysis. 16 (2009), 193-207 - O. A. Adesina,
*Demidovic's limiting regime to a certain fourth order nonlinear differential equation Another Results*. Journal of the Nigerian Mathematical Society, Vol. 31 (2012), 35-48 - A. U. Afuwape,
*Ultimate boundedness results for a certain system of third-order nonlinear differential equations*. J. Math. Anal. Appl., 97 (1983), 140-150 - A. U. Afuwape and M. O. Omeike,
*Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations.*Acta Univ. Palacki. Olumuc., Fac. rer. nat., Mathematica, 43 (2004), 7-20 - } A. U. Afuwape and M. O. Omeike,
*On the Existence of a limiting regime in the sense of Demidovic for a certain Third-order nonlinear differential equation*. Differentia Equations and Control Processes, Electronic Journal, no. 2 (2010), 40-55 - A. U. Afuwape,
*On the Existence of a limiting regime in the sense of Demidovic for a certain Fourth-order Nonlinear Differential Equation*. J. of Mathematical Analysis and Applications, 129 (1988), 389-393 - J. G. Alaba and B. S. Ogundare,
*On stability and boundedness properties of solutions of certain second order non-autonomous nonlinear ordinary differential equations*. Kragujevac Journal of Mathematics, 39, 2 (2015), 255-266 - M. L. Cartwright and J. E. Littlewood,
*On nonlinear differential equations of the second order*. Annali of Math., 48(1947), 472-494 - B. P. Demidovic,
*On the existence of a limiting regime of a certain nonlinear system of ordinary differential equations*. Amer. Math. Soc. Transl. ser., 18(2), 151-161. 1961 - J. O. C. Ezeilo and H. O. Tejumola,
*Boundedness and periodicity of solutions of a certain system of third-order non-linear differential equations*. Ann. Mat. Pura Appl. 66(1964) 283-316 - J. O. C. Ezeilo,
*Stability results for the solutions of some third and fourth order differential equations*. Ann. Mat. Pura Appl. 66(1964) 233-249 - J. O. C. Ezeilo,
*New properties of the equation*!!!! ERROR!!! IMAGE IS NOT ALLOWED!*for certain special values of the incrementary ratio*!!!! ERROR!!! IMAGE IS NOT ALLOWED!. Equations differentielles et fonctionnelles non linires ( Actes Conference internat " Equa-Diff 73", Brussels / Louvain-la-Neuve), Hermann, Paris, 447-462, 1973. MR0430413 (55#3418) - J. O. C. Ezeilo,
*A generalization of a result of Demidovic on the existence of a limiting regime of a system of differential equations*. Portugaliae Math. 25 (1965), 65-82 - J. O. C. Ezeilo,
*On the convergence of solutions of certain systems of second order equations*. Ann. Mat. Pura. Appl 72 (1966), 239-252 - G. A. Grigoryan,
*Boundedness and stability criteria for linear ordinary differential equations of the second order*. Russian Mathematics, 57, 12 (2013), 8-15 - A. J. Kroopnick,
*Bounded solutions to*!!!! ERROR!!! IMAGE IS NOT ALLOWED! International Journal of Mathematical Education in Science and Technology, 41, 6 (2010), 829-836 - A. J. Kroopnick,
*Two new proofs for the boundedness of solutions to $ x^{ \prime \prime} + a(t)x = 0$*. Missouri. J. Math. Sci. 25, 1(2013), 103-105 - A. J. Kroopnick,
*On the integration of*!!!! ERROR!!! IMAGE IS NOT ALLOWED!*-solutions of non-oscillatory solutions to*!!!! ERROR!!! IMAGE IS NOT ALLOWED!*.*Int. Math Forum 9, 10 (2014), 475-481 - W. S. Loud,
*Boundedness and convergence of solutions of*!!!! ERROR!!! IMAGE IS NOT ALLOWED!. Duke Math., J. 24 (1957), 63-72 - B. S. Ogundare, ~ A. T. Ademola, ~ M. O. Ogundiran and O. A. Adesina,
*On the qualitative behaviour of solutions to certain second order nonlinear differential equation with delay*. Annali dell' Universita' di Ferrara, 2016 - A. L. Olutimo,
*Existence of a limiting regime in the sense of Demidovic for a certain nonlinear differential equations of third order*. MAYFEB Journal of Mathematics- ISSN 2371-6193, vol. 4 (2017), 53-66 - M. O. Omeike, O. O. Oyetunde and A. L. Olutimo,
*Boundedness of solutions of certain systemof second-order ordinary differential equations*. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math., 53 (2014), 107-115 - H. O. Tejumola,
*Boundedness theorems for some systems of two differential equations*. Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 51, 6 (1971), 472-476 - H. O. Tejumola,
*Boundedness criteria for solutions of some second-order differential equations*. Atti Della Accademia Nazionale Dei Lincei Serie VII, 60, 2 (1976), 100-107 - C. Tunc and E. Tunc,
*On the asymptotic behaviour of solutions of certain second order differential equations*. J. Franklin Inst., 344(2007), 391-398 - C. Tunc and E. Tunc,
*On the boundedness of solutions of non-autonomous differential equations of second order*. Sarajevo Journal of Mathematics, 17(2011), 19-29 - C. Tunc and 0. Tunc,
*A note on certain qualitative properties of a second order linear differential system*. Appl. Math. Int. Sci. 9 (2), (2015), 953-956 - C. Tunc and O. Tunc,
*A note on the stability and boundedness of solutions to non-linear differential systems of second order*. J. Assoc. Arab Univ. Basic Appl. Sci., 24(2017), 169-175