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This paper is concerned with the existence and uniqueness of solutions to the second order distributional differential equation with Neumann boundary value problem via Henstock–Kurzweil–Stieltjes integrals.The existence of solutions is derived from Schauder’s fixed point theorem, and the uniqueness of solutions is established by Banach’s contraction principle. Finally, two examples are given to demonstrate the main results.

Existence and uniqueness of solutions to distributional differential equations involving Henstock–Kurzweil–Stieltjes integrals