M. Tvrdý

Differential and integral equations in the space of regulated functions

abstract:
The paper is devoted to generalized linear differential and integral equations with solutions in the class of regulated functions (i.e., functions which can have only discontinuities of the first kind). For generalized differential equations the problem on continuous dependence of solutions of the initial value problem on a parameter $k\in \Bbb{N}$ is considered, as well as the problem on solvability and Fredholm property of the generalized boundary problem. For generalized integral equations the problem on unique solvability is treated.

Mathematics Subject Classification: 34B05, 45A05.

Key words and phrases: Generalized differential equations, solvability, uniqueness, Fredholm alternative.