Becker, Leigh C. Uniformly continuous \(L^1\) solutions of Volterra equations and global asymptotic stability. (English) Zbl 1190.45010 Cubo 11, No. 3, 1-24 (2009). This paper concerns the following Volterra integro-differential equation \[ x'(t)= -a(t)x(t)+ \int^t_0 b(t,s) x(s)\,ds, \] where \(a\) and \(b\) are continuous functions. Lyapunov functions are constructed and they allow to obtain sufficient conditions so that the solutions of the given equation aer absolutely Riemann integrable on \([0,+\infty)\) and have bounded derivatives. By Barbalat’s lemma it has been proved that under certain hypotheses the zero solution is stable and that all solutions approach zero as \(t\to+\infty\). Reviewer: Sebastian Anita (Iaşi) Cited in 9 Documents MSC: 45M10 Stability theory for integral equations 45J05 Integro-ordinary differential equations 45D05 Volterra integral equations Keywords:asymptotic stability; Barbalat’s lemma; Lyapunov functions; Volterra integro-differential equations PDFBibTeX XMLCite \textit{L. C. Becker}, Cubo 11, No. 3, 1--24 (2009; Zbl 1190.45010)