Vol. 45, No. 1, 1973

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Asymptotic relations between perturbed linear systems of ordinary differential equations

Thomas Guy Hallam and Nelson Onuchic

Vol. 45 (1973), No. 1, 187–199

A generalization of the concept of asymptotic equivalence of two systems of ordinary differential equations is investigated. This extension of asymptotic equivalence is novel in two ways. First, the dimensions of the linear asymptotic subspaces of the differential equations are utilized. Secondly, the two Banach spaces L and L0, that are implicitly used in the usual definition of asymptotic equivalence, are replaced by two (arbitrary) Banach spaces that are stronger that L(X). The main theorem establishes a functional asymptotic relationship between the solutions of two perturbed linear differential equations that utilizes the above modifications.

Mathematical Subject Classification 2000
Primary: 34D10
Received: 11 October 1971
Published: 1 March 1973
Thomas Guy Hallam
Nelson Onuchic