Application of M-matrices in construction of exponential estimates for solutions to the Cauchy problem for systems of linear difference and differential equations

DOI10.3103/S1055134414040026zbMath1340.34179MaRDI QIDQ2945821

Nikolay Viktorovitch Pertsev

Publication date: 14 September 2015

Published in: Siberian Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

exponential stabilitynonnegative matrixsystem of linear difference equationsexponential estimatesystem of linear differential equationsmonotone methodnondegenerate M-matrixsystem of linear differential equations with aftereffect

Mathematics Subject Classification ID

Asymptotic theory of functional-differential equations (34K25) Linear ordinary differential equations and systems (34A30) Linear functional-differential equations (34K06) Asymptotic properties of solutions to ordinary differential equations (34D05) Stability theory for difference equations (39A30) Linear difference equations (39A06)

Related Items (5)

Application of differential equations with variable delay in the compartmental models of living systems ⋮ About exact two-sided estimates for stable solutions to autonomous functional differential equations ⋮ Asymptotic behavior of solutions in one predator-prey model with delay ⋮ Exponential decay estimates for some components of solutions to the nonlinear delay differential equations of the living system models ⋮ Exponent estimation for stable solutions of a certain class of differential-difference equations

Cites Work

• New stability conditions for linear differential equations with several delays
• Modeling population dynamics under the influence of harmful substances on the individual reproduction process
• Stability of solutions of autonomous Ważewski systems with delayed action
• Interaction between oscillations and global asymptotic stability in delay differential equations
• On exponential stability of linear differential equations with several delays
• Theory of functional differential equations. 2nd ed
• On exponential stability of linear difference-differential systems
• Time-delay systems: an overview of some recent advances and open problems.
• Stability conditions for systems of linear nonautonomous delay differential equations
• Exponential stability in a scalar functional differential equation
• Perron's theorem for linear impulsive differential equations with distributed delay
• Global attractivity in delay differential equations using a mixed monotone technique
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