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

Takasi Kusano

 Department of Mathematics, Faculty of Science, Hiroshima University, Hiroshima, Japan
Received 6 April 1982

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.