International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 559-566

Asymptotic relationships between two higher order ordinary differential equations

Takasi Kusano

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.


Some asymptotic relationships between the two ordinary differential equations (1)x(n)+p1(t)x(n1)++pn(t)x=0, (2)y(n)+p1(t)y(n1)++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.