Existence Of Solutions Of First Order Impulsive Dynamic Equations On Time Scales

The theory of dynamic equations on time scales is a new branch of mathematics which appears as a natural description of evolution phenomena of several real world problems. Existence of solutions is an important investigation area of dynamic equations. In this paper, a class of first-order delay impulsive dynamic equations is considered. The results given in this paper extend and improve the corresponding ones in the literatures.In Chapter 1, we introduce the fundamental concepts and theory of time scales and dynamic equations.In Chapter 2, we study the first-order delay impulsive dynamic equation with nonlinearfunctional boundary value conditionIn section 2, comparison results for first-order linear dynamic inequalityandare established and existence of unique solution to a class of nonlinear impulsive dynamic equationsis obtained.In section 3, by using method of upper and lower solutions and Schauder's fixed point theorem, some sufficient conditions for existence of at least one solution to problem (*) is obtained. In section 4, using monotone iterative technique, existence of extremal solutions to problem (*) is established.