Electron. J. Diff. Equ., Vol. 2009(2009), No. 161, pp. 1-13.

Existence of solutions and convergence results for dynamic initial value problems using lower and upper solutions.

Atiya H. Zaidi

In this article, we study the existence of solutions to first order non-linear initial value problems within the field of "dynamic equations on time scales". We employ the method of upper and lower solutions and Schauder's fixed point theorem. We also provide sufficient conditions under which the upper and lower solutions converge uniformly to a solution. Some examples are given to illustrate the new results.

Submitted November 24, 2009. Published December 17, 2009.
Math Subject Classifications: 34N05, 26E70.
Key Words: Existence of solutions; non-linear nabla equations; lower and upper solutions; zero approximations.

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Atiya H. Zaidi
School of Mathematics and Statistics
The University of New South Wales
Sydney NSW 2052, Australia
email: a.zaidi@unsw.edu.au

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