ALGORITHMS IN ASYMPTOTICAL THEORY OF SOLUTIONS OF EQUATIONS WITH RETARDED ARGUMENT

Abstract

The article deals with the problem of establishing the asymptotic behavior of solutions to initial problems for linear differential equations with bounded delay with an unbounded increase of time. In previously published papers, to systematically study such problems, the definition of asymptotic equivalence with infinite time increase was introduced for sets of functions defined on the half-axis: the distance between two solutions tends to zero. Also, calculations were carried out to experimentally determine the areas of coefficients of the equations that ensure the presence of asymptotic equivalence in the space of solutions, and to prove the presence of asymptotic equivalence in the space of solutions. The general technique for using a computer to establish the asymptotic behavior of solutions to initial problems for linear differential equations with bounded delay with an unlimited increase in time, proposed in this article, can be used for other problems.