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

Abstract

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.

Keywords

• Existence of solutions
• non-linear nabla equations
• lower and upper solutions
• zero approximations