| Title:
|
Oscillation of the third order Euler differential equation with delay (English) |
| Author:
|
Baculíková, Blanka |
| Author:
|
Džurina, Jozef |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
649-655 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper we offer criteria for oscillation of the third order Euler differential equation with delay $$ y'''(t)+\frac {k^2}{t^3}y(ct)=0. $$ We provide detail analysis of the properties of this equation, we fill the gap in the oscillation theory and provide necessary and sufficient conditions for oscillation of equation considered. (English) |
| Keyword:
|
third-order functional differential equation |
| Keyword:
|
Euler equation |
| Keyword:
|
oscillation |
| Keyword:
|
nonoscillation |
| MSC:
|
34C10 |
| MSC:
|
34K11 |
| idZBL:
|
Zbl 06433688 |
| idMR:
|
MR3306854 |
| DOI:
|
10.21136/MB.2014.144141 |
| . |
| Date available:
|
2015-02-04T09:23:04Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144141 |
| . |
| Reference:
|
[1] Arino, O., Győri, I.: Necessary and sufficient condition for oscillation of a neutral differential system with several delays.J. Differ. Equations 81 (1989), 98-105. Zbl 0691.34054, MR 1012201, 10.1016/0022-0396(89)90179-4 |
| Reference:
|
[2] Baculíková, B.: Properties of third-order nonlinear functional differential equations with mixed arguments.Abstr. Appl. Anal. 2011 (2011), Article No. 857860, 15 pages. Zbl 1217.34109, MR 2776748 |
| Reference:
|
[3] Cecchi, M., Došlá, Z., Marini, M.: On third order differential equations with property A and B.J. Math. Anal. Appl. 231 (1999), Article ID jmaa.1998.6247, 509-525. MR 1669163, 10.1006/jmaa.1998.6247 |
| Reference:
|
[4] Džurina, J.: Asymptotic properties of third order delay differential equations.Czech. Math. J. 45 (1995), 443-448. MR 1344509 |
| Reference:
|
[5] Džurina, J.: Comparison theorems for differential equations with deviating argument.Math. Slovaca 45 (1995), 79-89. Zbl 0830.34059, MR 1335843 |
| Reference:
|
[6] Kiguradze, I. T., Chanturia, T. A.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Mathematics and Its Applications (Soviet Series) 89 Kluwer Academic Publishers, Dordrecht (1993), translated from the 1985 Russian original. Zbl 0782.34002, MR 1220223, 10.1007/978-94-011-1808-8 |
| Reference:
|
[7] Kulenović, M. R. S.: Oscillation of the Euler differential equation with delay.Czech. Math. J. 45 (1995), 1-6. Zbl 0832.34069, MR 1314527 |
| Reference:
|
[8] Kusano, T., Naito, M.: Comparison theorems for functional-differential equations with deviating arguments.J. Math. Soc. Japan 33 (1981), 509-532. Zbl 0494.34049, MR 0620288, 10.2969/jmsj/03330509 |
| Reference:
|
[9] Kusano, T., Naito, M., Tanaka, K.: Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations.Proc. R. Soc. Edinb., Sect. A, Math. 90 (1981), 25-40. Zbl 0486.34021, MR 0636062, 10.1017/S0308210500015328 |
| Reference:
|
[10] Ladde, G. S., Lakshmikantham, V., Zhang, B. G.: Oscillation Theory of Differential Equations with Deviating Arguments.Monographs and Textbooks in Pure and Applied Mathematics 110 Marcel Dekker, New York (1987). Zbl 0832.34071, MR 1017244 |
| . |
