A. N. Rumyantsev

The constructive study of differential equations with deviated argument

A constructive technique for the study of linear differential equations with arbitrary deviations is considered. This technique allows to recognize the property of the correct solvability of the so called Principal Boundary Value Problem for a class of differential systems and $n$-th order differential equations, as well as to construct approximate solutions of such problems with guaranteed error bounds.

Mathematics Subject Classification: 34K07, 34A45, 34-04, 34K06, 34K46, 65L70.

Key words and phrases: Differential equations with deviated argument, the Cauchy problem, the principal boundary value problem, constructive methods, unique solvability, approximate solutions.