Geodesic
Exponential stability of autonomous differential equations of neutral type. I
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 12-28

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In this paper we consider linear differential equations of neutral type. We establish necessary and sufficient conditions under which the Cauchy function and the fundamental solution of these equations have exponential estimates. The obtained results reduce the problem of exponential stability for autonomous equation of neutral type to two simpler ones: on reversibility of the operator at the derivative and on the location of the zeros of the characteristic function on the complex plane, while it is not necessary to check the separation of the zeros of the characteristic function from the imaginary axis.
Mots-clés : neutral equation
Keywords: aftereffect, the Cauchy function, fundamental solution, exponential estimation, exponential stability. 
@article{IVM_2023_3_a1,
     author = {A. S. Balandin},
     title = {Exponential stability of autonomous differential equations of neutral type. {I}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--28},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_3_a1/}
}
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A. S. Balandin. Exponential stability of autonomous differential equations of neutral type. I. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 12-28. http://geodesic.mathdoc.fr/item/IVM_2023_3_a1/