This article is cited in 3 papers

Brief communications

On exact sufficient conditions of oscillation of solutions to linear differential and difference equations of the first order with aftereffect

K. M. Chudinov

Perm National Research Polytechnic University, 29 Komsomol'skii Ave., Perm, 614990 Russia

Abstract: We obtain new unimprovable effective conditions for the oscillation of 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 case exceptionally known approaches used.

Keywords: differential equation, difference equation, aftereffect, equation with several delays, oscillation, effective conditions.

UDC: 517.929

Received: 22.11.2017

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:5, 79–84

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