V. P. Maksimov

To the Question of Saving the Unique Solvability of the General Linear Boundary Value Problem for a Class of Functional Differential Systems with Discrete Memory

abstract:
A class of linear functional differential systems with continuous and discrete times and discrete memory is considered. The paper gives an explicit description of a family of uniquely solvable linear boundary value problems as a neighborhood of a fixed uniquely solvable boundary value problem. The description is based on an explicit representation of the principal components to the general solution representation such as the fundamental matrix and the Cauchy operator. In the study of the problems outside the class under consideration, the systems with discrete memory can be employed as a model or approximating ones. This can be useful as applied to systems with aftereffect under studying rough properties that hold under small disturbances of the parameters.

Mathematics Subject Classification: 34K10, 34K27, 34K34

Key words and phrases: Functional differential equations, continuous-discrete systems, linear boundary value problems, unique solvability conditions