On Exact Sufficient Oscillation Conditions for Solutions of Linear Differential and Difference Equations of the First Order With Aftereffect

摘要

We obtain new unimprovable effective oscillation conditions for all solutions of linear first-order differential and difference equations with several delays. We show that known results of the kind are consequences of the new results. We reveal the reasons for the impossibility to obtain oscillation conditions for equations with several delays, as sharp as the conditions for the equation with one delay, in the case when only known approaches are used.