Milan Tvrdy

Linear Integral Equations in The Space of Regulated Functions

In this paper, we investigate the existence of solutions to a wide class of systems of linear integral equations with solutions which can have in the closed interval [0,1] only discontinuities of the first kind and are left--continuous on the corresponding open interval (0,1). The results cower, e.g., the results knownfor systems of linear generalized differential equations as well as systems of Stieltjes Integral equations. Some possible applications to functional differential equationsare discussed as well.

Mathematics Subject Classification: } 45A05, 47G10, 26A39, 26A42.

Key words and phrases: Regulated function, Fredholm--Stieltjes integral equation, Voltera--Stieltjes integral equation, compact operator, Perron--Stieltjes integral, Kurzweil integral.