International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 249-256

Nonoscillation theorems for functional differential equations of arbitrary order

John R. Graef,1 Myron K. Grammatikopoulos,2 Yuichi Kitamura,3 Takaŝi Kusano,4 Hiroshi Onose,5 and Paul W. Spikes6

1Department of Mathematics and Statistics, Mississippi State University, Mississippi State, 39762, Mississippi, USA
2Department of Mathematics, University of Ioannina, loannina, Greece
3Department of Mathematics, Nagasaki University, Nagasaki 852, Japan
4Department of Mathematics, Hiroshima University, Hiroshima 730, Japan
5Department of Mathematics, Ibaraki University, Mito 310, Japan
6Department of Mathematics and Statistics, Mississippi State University, Mississippi State 39762, Mississippi, USA

Received 20 May 1983

Copyright © 1984 John R. Graef et al. 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.


The authors give sufficient conditions for all oscillatory solutions of a sublinear forced higher order nonlinear functional differential equation to converge to zero. They then prove a nonoscillation theorem for such equations. A few intermediate results are also obtained.