International Journal of Mathematics and Mathematical Sciences 
Volume 7 (1984), Issue 2, Pages 249-256
doi:10.1155/S0161171284000259

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

Abstract

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.