
Also note the comments. made on (1.1) in [2]. More recently Eq. (1.1) has been analyzed in [I and 31 under hypotheses related to those of Theorem I. Comparing the present result with the results of [3] we observe the following. In addition to the full hypothesis of Theorem 1 above, certain smoothness conditions were imposed on a(t) and f(i) in [3]. Specifically, a(t) E Cl[O, co) and absolute continuity of f(t) on [0, 00) were assumed. In the present result these requirements have been weakened, and in particular we do not even require a(t) to be continuous. A comparison with [l] yields roughly the following. At the expense of assuming the existence of a bounded solution we are able, in Theorem 1, to obtain results on the asymptotic behavior of the solutions under weaker hypotheses than in [l]. In particular we do neither make any assumption of type xg(x) > 0, nor do we require g(x) to satisfy a Lipschitz-type condition near the equilibrium point. Only continuity is imposed on g(x). As to the existence of bounded solutions we have the following result which partially overlaps the results of [ 11, and extends a result obtained in [3].
Volterra integral equations, Asymptotics of solutions to integral equations, Analysis
Volterra integral equations, Asymptotics of solutions to integral equations, Analysis
| citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 38 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 1% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
