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Journal of Differential Equations
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Journal of Differential Equations
Article . 1973
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Journal of Differential Equations
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On a nonlinear Volterra integral equation

Authors: Stig-Olof Londen;

On a nonlinear Volterra integral equation

Abstract

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].

Keywords

Volterra integral equations, Asymptotics of solutions to integral equations, Analysis

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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).
BIP!Citations provided by BIP!
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.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
38
Average
Top 1%
Top 10%
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