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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2017 Volume 132, Pages 135–138 (Mi into183)

Exact conditions of oscillation of solutions to differential equations with several delays

K. M. Chudinov

Perm State National Research Polytechnical University

Abstract: We obtain new nonimprovable conditions of oscillation of all solutions to a linear differential equation with several variable delays and positive coefficients. These condition have the form of the upper and lower limits of the sum of integrals of the coefficients over the sets that are determined only by the delay corresponding to this coefficient. These results differ from the well-known results in which a coarsening of the integration set is assumed.

Keywords: differential equation with several delays, oscillation, effective condition.

UDC: 517.929

MSC: 34K06, 34K11


 English version:
Journal of Mathematical Sciences (New York), 2018, 230:5, 790–793

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© Steklov Math. Inst. of RAS, 2025