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On nonlinear functional perturbation problems for ordinary differential equations

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
12
Issue
1
Identifiers
DOI: 10.1016/0022-0396(72)90005-8
Disciplines
  • Mathematics

Abstract

Abstract The linear homogeneous system of differential equations is a good basic model for perturbation problems because many useful properties of the solutions of linear equations are readily established. In this article, conditions are imposed upon a linear system of differential equations which imply that the linear system is either conditionally uniformly stable, conditionally asymptotically stable, or conditionally uniformly asymptotically stable. Then, a class of perturbation, terms is found which asymptotically preserves the solutions of the linear system that satisfy a prescribed growth condition. The class of perturbation terms is sufficiently general to include functions which possess retarded, advanced, or a combination of retarded and advanced arguments.

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