Perturbation theorems for functional differential equations with infinite delay via limiting equations

DOI10.1016/0022-0396(85)90144-5zbMath0565.34059OpenAlexW2031891469MaRDI QIDQ1058653

Satoru Murakami

Publication date: 1985

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(85)90144-5

zbMATH Keywords

perturbationinfinite delayuniform asymptotic stabilityfunctional differential equationslimiting equations

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (17)

Uniform asymptotic stability in perturbed differential equations ⋮ Method of limiting equations for the stability analysis of equations with infinite delay in the Carathéodory conditions. I ⋮ Liapunov-Razumikhin pairs and the location of positive limit sets for precompact functional differential equations with infinite delay ⋮ Existence of periodic solutions to integro-differential equations of neutral type via limiting equations ⋮ Development of the direct Lyapunov method for functional-differential equations with infinite delay ⋮ Lyapunov functional method in the stability problem of Volterra integro-differential equations with infinite delay ⋮ On the principle of reduction for the nonlinear delay systems ⋮ A priori bounds and stability in the retarded nonlinear wave equation ⋮ On the stability of nonautonomous functional differential equation ⋮ The method of Lyapunov functionals in stability analysis of functional-differential equations ⋮ Invariance principles and asymptotic constancy of solutions of precompact functional differential equations ⋮ Local and semiglobal stabilization in a cascade with delay ⋮ Lyapunov functionals of constant signs in the stability problem for a functional-differential equation of neutral type ⋮ Method of limiting equations for the stability analysis of equations with infinite delay in the Carathéodory conditions. II ⋮ On the Stability and Stabilization Problems of Volterra Integro-Differential Equations ⋮ The Lyapunov functionals method in stability problems for functional differential equations ⋮ The method of Lyapunov-Razumikhin functions in stability analysis of systems with delay

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• Stability properties for functional differential equations with infinite delay
• Exponential asymptotic stability for functional differential equations with infinite retardations
• Lyapunov theory and perturbation of stable and asymptotically stable systems
• Uniform asymptotic stability via the limiting equations
• Almost periodic solutions and asymptotic stability
• Perturbing uniform asymptotically stable nonlinear systems
• Perturbation theorems for ordinary differential equations
• Uniformly asymptotic stability and total stability
• Limiting equations in the stability problem
• Perturbing Uniformly Stable Linear Systems with and without Attraction

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