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Proceedings of the American Mathematical Society

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



Bounds for solutions of perturbed differential equations

Author: T. G. Proctor
Journal: Proc. Amer. Math. Soc. 45 (1974), 73-79
MSC: Primary 34D10; Secondary 34A10
MathSciNet review: 0344615
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Abstract: A modified form of the Alekseev variation of constants equation is used to relate the solutions of systems of the form $ \dot x = f(t,x,\lambda ),\lambda $ in $ {R^m}$ and the perturbed system $ \dot y = f(t,y,\psi (t)) + g(t,y)$. Hypotheses are given on the $ m$ parameter family of differential equations $ \dot x = f(t,x,\lambda )$ so that if $ \dot \psi $ and $ g$ are perturbation functions, bounds can be calculated for the solutions of the perturbed system.

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Keywords: Perturbed differential equations, Alekseev formula, bounds, comparison theorems, Volterra integral equations
Article copyright: © Copyright 1974 American Mathematical Society