Existence and uniqueness of solutions to distributional differential equations involving Henstock-Kurzweil-Stieltjes integrals. (English) Zbl 1432.34005
Summary: 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.
MSC:
| 34A06 | Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 26A42 | Integrals of Riemann, Stieltjes and Lebesgue type |
| 47N20 | Applications of operator theory to differential and integral equations |
