MR2108672 Sedova, N. O. N. O. SEDOVA Razumikhin-Type Theorems in the Problem on Instability of Nonautonomous Equations with Finite Delay Funkcialaj Ekvacioj. Serio Internacia 47 2004 187--204 http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-2/47_187.pdf http://www.ams.org/mathscinet-getitem?mr=MR2108672 The paper provides some theorems on complete instability of zero solution relative to a set for nonautonomous nonlinear equations with delay. The right-hand side of the equation is assumed to satisfy conditions, which provide standard existence-uniqueness-continuous dependence-continuation theory for the equation, as well as precompactness of the collection of translations in time of the right-hand side in a functional space with a metrizable compact open topology. These assumptions allow constructing limiting equations. Using conceptions of Lyapunov-Razumikhin functions and limiting equations, new instability results are obtained, which are applicable, in particular, to autonomous and periodic delayed differential equations and generalize some known results. Nonlinear equations with delay, Instability, Lyapunov-Razumikhin functions, Limiting equations. 34K20. 47-187 2004 Razumikhin-Type Theorems in the Problem on Instability of Nonautonomous Equations with Finite Delay SEDOVA, N. O. N. O. SEDOVA
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