A framework for asymptotic integration of differential systems

Article type: Research Article

Authors: Elias, Uri | Gingold, Harry

Affiliations: Department of Mathematics, Technion, I.I.T., Haifa 32000, Israel E‐mail: [email protected] | Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA E‐mail: [email protected]

Abstract: A new method for asymptotic integration of linear systems of ordinary differential equations is proposed and studied. It is based on the introduction of a certain integral equation that pinpoints sufficient conditions for asymptotic integration. These conditions serve as a framework from which new and old theorems are derived. In particular the fundamental theorems of Levinson and Hartman–Wintner are shown to follow from one and the same scheme. The new theorems in asymptotic integration are shown to be best possible in a certain sense. Examples are given that are not amenable to other techniques.

Journal: Asymptotic Analysis, vol. 35, no. 3-4, pp. 281-300, 2003