International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 559-566
doi:10.1155/S0161171283000514
Asymptotic relationships between two higher order ordinary differential equations
Department of Mathematics, Faculty of Science, Hiroshima University, Hiroshima, Japan
Received 6 April 1982
Copyright © 1983 Takasi Kusano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Some asymptotic relationships between the two ordinary differential equations
(1) x(n)+p1(t)x(n−1)+…+pn(t)x=0,
(2) y(n)+p1(t)y(n−1)+…+pn(t)y=f(t,y),
are studied. Conditions are given that lead to an asymptotic equivalence between certain of the solutions of (1) and certain of the solutions of (2). The case where the perturbation f(t,y) depends on a functional argument is also discussed.