Existence Theorem for Abstract Measure Differential Equations Involving the Distributional Henstock-Kurzweil Integral

摘要

In this paper, we study the existence of solutions of the abstract measure differential equations by using the Leray-Schauder’s nonlinear alternative and distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is very general and it includes the Lebesgue integral and Henstock-Kurzweil integral. The main result of the paper extends some previously known results in the literature.