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Asymptotic Integration for Differential Systems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2129)

Abstract

In this chapter we are concerned with the following general problem: If we are given a linear system

$$\displaystyle{ y' = \left [A(t) + R(t)\right ]y,\qquad t \geq t_{0}, }$$
(2.1)

and “know” a fundamental solution matrix X(t) for the (unperturbed) system x′ = A(t)x, how “small” should the perturbation R(t) be so that we can determine an asymptotic behavior for solutions of (2.1)? This question is intentionally vague because depending upon the particular circumstances, there are many possible answers.

Keywords

  • Asymptotic Integration
  • Fundamental Matrix Solution
  • Exponential Dichotomy
  • Stronger Dichotomy Conditions
  • Ordinary Duality

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bodine, S., Lutz, D.A. (2015). Asymptotic Integration for Differential Systems. In: Asymptotic Integration of Differential and Difference Equations. Lecture Notes in Mathematics, vol 2129. Springer, Cham. https://doi.org/10.1007/978-3-319-18248-3_2

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