On the Darboux problem involving the distributional Henstock–Kurzweil integral

Abstract

Abstract In this paper, we apply the method associated with the technique of measure of noncompactness and the Darbo fixed point theorem to study the existence of solutions of the Darboux problem involving the distributional Henstock–Kurzweil integral. Meanwhile, an example is provided to illustrate our results.

Keywords

• Darboux problem
• Distributional Henstock–Kurzweil integral
• Measure of noncompactness
• Darbo fixed point theorem