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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A variation-of-parameters inequality


Author: David Lowell Lovelady
Journal: Proc. Amer. Math. Soc. 26 (1970), 598-602
MSC: Primary 34D05
DOI: https://doi.org/10.1090/S0002-9939-1970-0435526-9
MathSciNet review: 0435526
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Abstract: Recent work in stability theory for linear ordinary differential equations has made much use of the inequalities which can be deduced from the variation-of-parameters formula. In this article it is shown that similar inequalities hold for nonlinear Stieltjes integral equations and hence, as a special case, for nonlinear differential equations in which the nonlinearity is of Lipschitz type.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0435526-9
Keywords: Bounds, nonhomogeneous perturbations, stability, Stieltjes integral equations, variation-of-parameters
Article copyright: © Copyright 1970 American Mathematical Society