Qualitative analysis of integro-differential equations with variable retardation
Martin Böhner, Osman Tunç
Abstract
<p style='text-indent:20px;'>The paper is concerned with a class of nonlinear time-varying retarded integro-differential equations (RIDEs). By the Lyapunov–Krasovski$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{ı} $ functional method, two new results with weaker conditions related to uniform stability (US), uniform asymptotic stability (UAS), integrability, boundedness, and boundedness at infinity of solutions of the RIDEs are given. For illustrative purposes, two examples are provided. The study of the results of this paper shows that the given theorems are not only applicable to time-varying linear RIDEs, but also applicable to time-varying nonlinear RIDEs.</p>
Topics & Concepts
MathematicsNonlinear systemStability (learning theory)InfinityVariable (mathematics)Class (philosophy)Differential equationApplied mathematicsMathematical analysisComputer sciencePhysicsMachine learningQuantum mechanicsArtificial intelligenceNonlinear Differential Equations AnalysisDifferential Equations and Numerical MethodsFractional Differential Equations Solutions