Existence of solutions of the wave equation involving the distributional Henstock-Kurzweil integral

Abstract

In this paper we study the application of a general integral called a distributional Henstock-Kurzweil integral which includes the Henstock-Kurzweil integral and the wide Denjoy integral. We prove the existence of solutions of the wave equation involving the distributional Henstock-Kurzweil integral by using Schauder's fixed-point theorem.