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Home  >  Volume 26 (March 2014)

10. On Application of ARZELA ̀-ASCOLI’S Theorem To Guarantee The Existence And Uniqueness of Local Solutions for an Initial Value Problem of a First Order Linear Differential Equation by EzeEverestusObinwanne. Volume26, (March, 2014), pp50 – 53.
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If a sequence of functions converges uniformly to a function y(t), then this function is a solution to our initial value problem; also there must exist a subsequence of the function which converges to the same y(t) being also a solution to our initial value problem provided that f is continuous (smooth rough). This point is a unique solution and uniqueness of the solution confirms existence of the solution but the converse is not time. In this paper, our objective is to use the theorem of Arzela ̀ Ascoli’s to prove the existence and uniqueness of a local solution to an initial value problem of first order linear differential equation. The results were shown to exist and thus confirms the existence of a local solution if and only if f is continuous.

Keywords:Arzela ̀-Ascoli theorem, Compactness, Equi-continuous, Boundedness, Uniform Convergence.AMS (2000) subject classification 03F10