Asymptotic stability properties of linear Volterra integrodifferential equations

Stability criteria for Volterra equations

“…Stability definitions given below are from Driver [4] and Miller [9]. Existence, uniqueness, and continuation results are found in Driver [4].…”

Transient behaviour and stability points of the Poiseuille flow of a KBKZ-fluid

“…The behaviour of the perturbed solution for t > to determines the stability of the unperturbed solution: If the perturbed solution remains bounded (or tends to zero) then the unperturbed solution is (asymptotically) stable. The definitions of stability of solutions of integrodifferential equations used here are similar to the usual definitions for ordinary differential equations (see [5], [6] and [7]). …”

New results on exponential stability of nonlinear Volterra integro-differential equations with constant time-lag

“…It is well known that while Lyapunov functions are made use in the investigation of (ODEs), more generally (LFs) are used in studying (FDEs) and (IDEs) (see, for example, Burton [6,7]. As (VIDEs) can also be treated as (FDEs), (LFs) have been constructed or defined exclusively for various (VIDEs) by Adıvar and Raffoul [1], Becker ([2], [3], [4]), Burton [5,6,7], Burton et al [8], Burton and Mahfoud ([9], [10]), Corduneanu [11], Diamandescu [12], Eloe et al [13], Furumochi and Matsuoka [14], Graef and Tunç [15], Graef et al [16], Grimmer and Seifert [17], Gripenberg et al [18], Hara et al [19], Islam and Raffoul [20], Jordan [21], Levin [22], Mahfoud [23], Miller [24], Raffoul [25], [26], [27], Raffoul and Ren [28], Raffoul and Unal [29], Rama Mohana Rao and Raghavendra [30], Rama Mohana Rao and Srinivas [31], Staffans [32], Tunç ([33], [34], [35]), Tunç and Ayhan [38], Vanualailai and Nakagiri [39], Wang [40], Wazwaz [41], Zhang [42], Da Zhang [43] and many relative papers in their references...…”