Abstract
In this article, we investigate existence of solutions for perturbed abstract measure functional differential equations. Based on the Arzela-Ascoli theorem and the fixed point theorem, we give sufficient conditions for existence of solutions for a class of perturbed abstract measure functional differential equations. Our system includes the systems studied in some previous articles as special cases and our sufficient conditions for existence of solutions are less conservative. An example is given to illustrate the effectiveness of our existence theorem of solutions.
Highlights
1 Introduction Abstract measure differential equations are more general than difference equations, differential equations, and differential equations with impulses
The study of abstract measure differential equations was initiated by Sharma [1] in 1970s
Properties of abstract measure differential equations have been researched by various authors
Summary
Abstract measure differential equations are more general than difference equations, differential equations, and differential equations with impulses. Properties of abstract measure differential equations have been researched by various authors. There were only some limited results on abstract measure differential equations can be found, such as existence [2,3,4,5,6], uniqueness [2,3,5], and extremal solutions [3,4,6].
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