Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1974-0344615-2
MathSciNet review: 0344615
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34D10, 34A10

Retrieve articles in all journals with MSC: 34D10, 34A10


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