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On Stieltjes-Volterra integral equations

Published online by Cambridge University Press:  17 April 2009

S.G. Pandit
S.G. Pandit
Affiliation:
Department of Mathematics, Centre of Post-Graduate Instruction and Research, University of Bombay, Panaji, Goa, India.
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Abstract

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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

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 3 , June 1978 , pp. 321 - 334
Copyright
Copyright © Australian Mathematical Society 1978

References

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