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- W2159729912 abstract "A Stieltjes-Volterra integral equation system is firstly considered. Pointwise estimates and boundedness of its solutions are obtained under various conditions on the function K . To do this, the well-known Gronwall-Bellman integral inequality is generalized. For a particular choice of u , it is shown that the integral equation reduces to a difference equation. The problem of existence (and non-existence), uniqueness (and non-uniqueness) of the difference equation is discussed. Gronwall-Bellman inequality is further generalized to n linear terms and is subsequently applied to obtain sufficient conditions in order that a certain stability of the unperturbed Volterra system implies the corresponding local stability of the (discontinuously) perturbed system" @default.
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- W2159729912 date "1978-06-01" @default.
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- W2159729912 title "On Stieltjes-Volterra integral equations" @default.
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- W2159729912 doi "https://doi.org/10.1017/s0004972700008200" @default.
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