| Title:
|
Oscillatory and asymptotic behaviour of solutions of advanced functional equations (English) |
| Author:
|
Džurina, Jozef |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
161-166 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we compare the asymptotic behaviour of the advanced functional equation \[ L_nu(t)-F\big (t,u[g(t)]\big )= 0\] with the asymptotic behaviour of the set of ordinary functional equations \[ \alpha _iu(t)-F\big (t,u(t)\big )= 0. \] On the basis of this comparison principle the sufficient conditions for property (B) of equation (*) are deduced. (English) |
| Keyword:
|
comparison theorem |
| Keyword:
|
advanced argument |
| Keyword:
|
property (B) |
| MSC:
|
34C10 |
| MSC:
|
34K15 |
| MSC:
|
34K99 |
| idZBL:
|
Zbl 0811.34052 |
| idMR:
|
MR1263117 |
| . |
| Date available:
|
2008-06-06T21:24:32Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107478 |
| . |
| Reference:
|
[1] Foster, K. E., Grimmer, R. C.: Nonoscillatory solutions of higher order differential equations.J. Math. Anal. Appl. 71 (1979), 1-17. MR 0545858 |
| Reference:
|
[2] Hille, E.: Non-oscillation theorems.Trans. Amer. Math. Soc. 64 (1948), 234-258. Zbl 0031.35402, MR 0027925 |
| Reference:
|
[3] Kiguradze, I. T.: On the oscillation of solutions of the equation $d^mu/dt^m + a(t)|u|^n sign\,u = 0$.Mat. Sb. 65 (1964), 172-187. (Russian) Zbl 0135.14302, MR 0173060 |
| Reference:
|
[4] Kusano, T., Naito, M.: Comparison theorems for functional differential equations with deviating arguments.J. Math. Soc. Japan 3 (1981), 509-532. MR 0620288 |
| Reference:
|
[5] Kusano, T., Naito, M., Tanaka, K.: Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations.Proc. Roy. Soc. Edinburg 90 (1981), 25-40. MR 0636062 |
| Reference:
|
[6] Trench, W. F.: Canonicals form and principal systems for general disconjugate equations.Trans. Amer. Math. Soc. 189 (1974), 319-327. MR 0330632 |
| . |
