Explicit solutions of linear Stieltjes integral equations

Abstract

We improve known results on the existence and uniqueness of solutions for two types of scalar linear Stieltjes integral equations, which are adjoint to each other. The main results are explicit solution formulas for homogeneous as well as nonhomogeneous problems.

Keywords

• Stieltjes integral equation
• Kurzweil-Stieltjes integral
• explicit solution formula
• existence and uniqueness of solutions