Geodesic
On the problem of the stability of functional-differential equations with infinite delay
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 29-38

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We study the stability of functional differential equations with infinite delay, using the Lyapunov functional of constant sign with a derivative of constant sign. Limit equations are constructed in a special phase space. We establish a theorem on localization of a positive limit set and theorems on the stability and the asymptotic stability. The results are illustrated by examples.
Keywords: functional differential equation, infinite delay, Lyapunov functional of constant sign
Mots-clés : limit equations. 
@article{IVM_2008_7_a3,
     author = {S. V. Pavlikov},
     title = {On the problem of the stability of functional-differential equations with infinite delay},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {29--38},
     publisher = {mathdoc},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_7_a3/}
}
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S. V. Pavlikov. On the problem of the stability of functional-differential equations with infinite delay. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 29-38. http://geodesic.mathdoc.fr/item/IVM_2008_7_a3/