Geodesic
Exponent estimation for stable solutions of a certain class of differential-difference equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 67-79

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For differential-difference equations with a positive fundamental solution we obtain exponential stability conditions with exact estimates of the exponent and coefficient of decay. The estimates are determined through the largest of two possible real roots of the characteristic function. We show that it is possible to obtain exact estimates for any solution, based on an estimate of the fundamental solution, and taking into account the norm of an initial function. We find two-sided estimates of the fundamental solution in the case when the parameters of an equation are given at intervals.
Keywords: functional differential equation, fundamental solution, exponential stability, exponent estimate. 
@article{IVM_2021_12_a5,
     author = {V. V. Malygina},
     title = {Exponent estimation for stable solutions of a certain class of differential-difference equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--79},
     publisher = {mathdoc},
     number = {12},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_12_a5/}
}
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V. V. Malygina. Exponent estimation for stable solutions of a certain class of differential-difference equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 67-79. http://geodesic.mathdoc.fr/item/IVM_2021_12_a5/