Vol. 70, No. 1, 1977

Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Asymptotic properties of nonoscillatory solutions of differential equations with deviating argument

Ch. G. Philos and V. A. Staïkos

Vol. 70 (1977), No. 1, 221–242
Abstract

Recently, there is an increasing interest in studying the n-th order differential equations involving the so called n-th order r-derivative of x

(rn−1(t)(rn−2(t)(⋅⋅⋅(r1(t)(r0(t)x(t))′)′⋅⋅⋅ )′)′)′

which causes damped terms. Here, the asymptotic behavior of nonoscillatory solutions of such general differential equations with deviating argument is studied and, more precisely, sufficient conditions which guarantee that

 lim x(t) = 0
t→∞

for the bounded nonoscillatory solutions x(t) are established. A basic theorem is obtained for the general case and then it is specialized into four corollaries concerning the particular case

rj = 1  for  j ⁄= n − N and  rn−N = r  (1 ≦ N ≦ n− 1)

which is of special interest. Finally, some examples are given to illustrate the significance of the results.

Mathematical Subject Classification 2000
Primary: 34K20
Milestones
Received: 16 March 1976
Revised: 19 January 1977
Published: 1 May 1977
Authors
Ch. G. Philos
V. A. Staïkos