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 in and the perturbed system . Hypotheses are given on the parameter family of differential equations so that if and are perturbation functions, bounds can be calculated for the solutions of the perturbed system.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0344615-2

Keywords:
Perturbed differential equations,
Alekseev formula,
bounds,
comparison theorems,
Volterra integral equations

Article copyright:
© Copyright 1974
American Mathematical Society