Geodesic
On stability of a~differential equation with aftereffect
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2014), pp. 25-41

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We obtain conditions of exponential and uniform stability for a solution of a linear differential equation with bounded aftereffect, in the form of domains in the parameter space. We construct examples that show exactness of boundaries of stability domains for two classes of functional differential equations, with concentrated and distributed delay. Along with classic methods of functional analysis and theory of functions we use the test-equations method.
Keywords: functional differential equation, aftereffect, stability, Cauchy function
Mots-clés : test equation. 
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     author = {T. L. Sabatulina and V. V. Malygina},
     title = {On stability of a~differential equation with aftereffect},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {25--41},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_4_a3/}
}
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T. L. Sabatulina; V. V. Malygina. On stability of a~differential equation with aftereffect. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2014), pp. 25-41. http://geodesic.mathdoc.fr/item/IVM_2014_4_a3/