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 | References | Similar Articles | Additional Information

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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Additional Information

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