Function bounds for solutions of Volterra equations and exponential asymptotic stability

DOI10.1016/j.na.2006.05.016zbMath1117.45003OpenAlexW2038831141MaRDI QIDQ880306

Leigh C. Becker

Publication date: 15 May 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.05.016

zbMATH Keywords

exponential asymptotic stabilityvariation of parametersGronwall's inequalitylinear Volterra integro-differential equationfunction bounds

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Asymptotics of solutions to integral equations (45M05) Stability theory for integral equations (45M10) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (13)

Unnamed Item ⋮ On uniform asymptotic stability of nonlinear Volterra integro-differential equations ⋮ On exponential stability of Volterra differential equations with delay ⋮ A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations ⋮ Mean square exponential and non-exponential asymptotic stability of impulsive stochastic Volterra equations ⋮ Unnamed Item ⋮ New results on exponential stability of nonlinear Volterra integro-differential equations with constant time-lag ⋮ New stability criteria for linear Volterra time-varying integro-differential equations ⋮ Stability of nonlinear Volterra equations and applications ⋮ New stability criteria for nonlinear Volterra integro-differential equations ⋮ Resolvents and solutions of singular Volterra integral equations with separable kernels ⋮ POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS ⋮ On positivity and stability of linear time-varying Volterra equations

Cites Work

• Ordinary and delay differential equations
• Inequalities for differential and integral equations
• Ordinary Differential Equations
• Volterra integral and differential equations
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