Affiliation:
1. Yaroslavl State University
Abstract
In this paper we study the oscillation problem for the known scalar
delay differential equation. We assume that the coefficients of this
equation have an oscillatory behaviour with an amplitude of oscillation
tending to zero at infinity. The asymptotic formulae for the solutions of
the considered equation in the so-called critical case are constructed. We
give the conditions for existence of oscillatory or nonoscillatory
solutions in terms of certain numerical quantities. The obtained results
are illustrated by a number of examples.