Introduction to Halanay Lemma, via Weakly Picard Operator Theory

DOI10.1007/978-3-030-60622-0_20zbMath1491.34089OpenAlexW3197252871MaRDI QIDQ5153569

Ioan A. Rus, Adrian Petruşel

Publication date: 30 September 2021

Published in: Approximation Theory and Analytic Inequalities (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-60622-0_20

zbMATH Keywords

asymptotic stabilityweakly Picard operatorabstract Gronwall lemmastep by step contractionconcrete Gronwall lemmaBurton method of progressive contractionsfunctional differential equations with maximaHalanay lemmaHalanay-type lemmas

Mathematics Subject Classification ID

Asymptotic theory of functional-differential equations (34K25) Applications of operator theory to differential and integral equations (47N20) Inequalities involving derivatives and differential and integral operators (26D10) Functional-differential inequalities (34K38)

Cites Work

• New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems
• Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag
• Ordinary and delay differential equations
• Im memoriam Aristide Halanay (1924-1997)
• Existence and stability of almost periodic solutions for quasilinear delay systems and the Halanay inequality
• A generalized Halanay inequality for stability of nonlinear neutral functional differential equations
• Differential equations: Stability, oscillations, time lags
• Dissipativity and asymptotic stability of nonlinear neutral delay integro-differential equations
• On the functional differential equations with “maximums”
• Sharp estimation for the solutions of inhomogeneous delay differential and Halanay type inequalities
• A note on existence and uniqueness for integral equations with sum of two operators: progressive contractions
• Abstract Volterra equations: a survey
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