ON THE STABILITY AND UNIQUE STABLE T- PERIODIC SOLUTION FOR REGULAR PERTURBATION SYSTEM FOR CERTAIN CLASS OF ORDINARY DIFFERENTIAL EQUATIONS

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EBIENDELE EBOSELE PETER
NOSAKHARE UWADIA FIDELIS

Abstract

The objective of this paper is to investigate a Regular Perturbation dynamic system of the type, non- autonomous type of  an ordinary differential equations of the form; x′ = f(x) + εg(x,t,ε),  and to establish the sufficient and necessary conditions for the differences between the dynamics for which ε = 0 and  ε > 0, and also establish x*  as a stable equilibrium point of the unperturbed autonomous system of  x′ = f(x)  The paper further establish, that the above given equation, admit a stable T- Periodic orbit in a neighborhood of x*. Some properties of the Hamiltonian  system, which form important source of the differential equations given above provided the motivation for the study. Proposition 1.1, Example 2.1, 2.2, 4.1, Theorem3.1 corollary3.1and Theorem 3.2 gives the results that established the objective for the study. My approach in this study has advantage over (3) and the results obtained in this study generalize the results in (3) in the case where four arguments were proved.

Keywords:
Stability, T-periodic, regular perturbation and differential equations.

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How to Cite
PETER, E., & FIDELIS, N. (2019). ON THE STABILITY AND UNIQUE STABLE T- PERIODIC SOLUTION FOR REGULAR PERTURBATION SYSTEM FOR CERTAIN CLASS OF ORDINARY DIFFERENTIAL EQUATIONS. Journal of Basic and Applied Research International, 25(1), 53-61. Retrieved from https://www.ikprress.org/index.php/JOBARI/article/view/4519
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Original Research Article