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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Perturbations of nonlinear differential equations


Authors: R. E. Fennell and T. G. Proctor
Journal: Trans. Amer. Math. Soc. 185 (1973), 401-411
MSC: Primary 34D10
DOI: https://doi.org/10.1090/S0002-9947-1973-0361309-1
MathSciNet review: 0361309
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Abstract: Scalar and vector comparison techniques are used to study the comparative asymptotic behavior of the systems (1) $ x' = f(t,x)$ and (2) $ y' = f(t,y) + g(t,y)$. Conditions are given which allow bounds for the solutions of (2) to be obtained assuming a knowledge of the solutions of (1) and which guarantee the generalized asymptotic equivalence of (1) and (2). Examples are given.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0361309-1
Keywords: Asymptotic behavior, perturbed nonlinear differential equations, bounds, comparison theorems, generalized asymptotic equivalence
Article copyright: © Copyright 1973 American Mathematical Society