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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Perturbations of solutions of Stieltjes integral equations

Author: David Lowell Lovelady
Journal: Trans. Amer. Math. Soc. 155 (1971), 175-187
MSC: Primary 45L05
MathSciNet review: 0433175
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Abstract: Using multiplicative integration in two ways, formulae for solutions to perturbed Stieltjes integral equations are found in terms of unperturbed solutions. These formulae are used to obtain bounds on the difference between the perturbed solution and the unperturbed solution. The formulae are also used to explicitly solve, in terms of product integrals, a linear equation subject to nonlinear interface conditions.

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Keywords: Perturbations, product integrals, bounds, stability, interface conditions
Article copyright: © Copyright 1971 American Mathematical Society