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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2023 Number 4, Pages 3–14 (Mi ivm9865)

Exponential stability of autonomous differential equations of neutral type. II

A. S. Balandin

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

Abstract: In this paper we consider linear differential equations of neutral type. We establish criteria for the solvability of the operator with a derivative in the spaces $L_p$, expressed in terms of the equation parameters, for commensurable delays and for delays linearly independent with respect to integers.

Keywords: neutral equation, aftereffect, the Cauchy function, fundamental solution, exponential estimations, exponential stability.

UDC: 517.929

Received: 24.05.2022
Revised: 24.05.2022
Accepted: 21.12.2022

DOI: 10.26907/0021-3446-2023-4-3-14



© Steklov Math. Inst. of RAS, 2024