Russian Mathematics · 2008 · 50 citations · 2 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsContinuous Dynamical SystemsExistence TheoryInitial Value ProblemsNumerical StabilityStability TheoryTime Delay EffectsDelay-dependent StabilityDelay-dependent Stability AnalysisDelay-dependent Stability CriteriaDelay-induced Stability AnalysisFunctional Differential SystemsFunctional EquationsStability Of Functional Differential Equations
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.
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