Geodesic
Stability in Part of the Variables of ``Partial'' Equilibria of Systems with Aftereffect
Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 496-503

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The problem of stability in part of the variables of a “partial” equilibrium (this means that a given part of the phase vector coordinates is zero) is considered for nonlinear nonstationary systems of functional differential equations with aftereffect. The notions of stability in part of the variables, which admit more general (compared with the known ones) assumptions about the values of the supremum-norm of the components of the initial vector function corresponding to the variables that do not determine the given equilibrium, are introduced. The stability and asymptotic stability conditions of the the type mentioned above are obtained in the context of the method of Lyapunov–Krasovskii functionals; this conditions allow generalization of several well-known results.
Keywords: stability in part of the variables, “partial” equilibrium, functional differential equations with aftereffect. 
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     author = {V. I. Vorotnikov and Yu. G. Martyshenko},
     title = {Stability in {Part} of the {Variables} of {``Partial''} {Equilibria} of {Systems} with {Aftereffect}},
     journal = {Matemati\v{c}eskie zametki},
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V. I. Vorotnikov; Yu. G. Martyshenko. Stability in Part of the Variables of ``Partial'' Equilibria of Systems with Aftereffect. Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 496-503. http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a1/