| Title:
|
On asymptotic behavior of solutions of $n$-th order Emden-Fowler differential equations with advanced argument (English) |
| Author:
|
Koplatadze, R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
817-833 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study oscillatory properties of solutions of the Emden-Fowler type differential equation $$u^{(n)}(t)+p(t)\big |u(\sigma (t))\big |^\lambda \operatorname{sign} u(\sigma (t))=0,$$ where $0<\lambda <1$, $p\in L_{\rm loc }(\Bbb R_+;\Bbb R)$, $\sigma \in C(\Bbb R_+;\Bbb R_+)$ and $\sigma (t)\ge t$ for $t\in \Bbb R_+$. \endgraf Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. \endgraf Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998). (English) |
| Keyword:
|
proper solution |
| Keyword:
|
property {\bf A} |
| Keyword:
|
property {\bf B} |
| MSC:
|
34C10 |
| MSC:
|
34K11 |
| MSC:
|
34K15 |
| idZBL:
|
Zbl 1224.34214 |
| idMR:
|
MR2672417 |
| . |
| Date available:
|
2010-07-20T17:21:14Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140606 |
| . |
| Reference:
|
[1] Kiguradze, I., Stavroulakis, I.: On the oscillation of solutions of higher order Emden-Fowler advanced differential equations.Appl. Anal. 70 (1998), 97-112. Zbl 1013.34068, MR 1671550, 10.1080/00036819808840679 |
| Reference:
|
[2] Kondrat'ev, V. A.: Oscillatory properties of solutions of the equation $y\sp{(n)}+p(x)y=0$.Russian Trudy Moskov. Mat. Obsc. 10 (1961), 419-436. MR 0141842 |
| Reference:
|
[3] Koplatadze, R.: On oscillatory solutions of second order delay differential inequalities.J. Math. Anal. Appl. 42 (1973), 148-157. Zbl 0255.34069, MR 0322313, 10.1016/0022-247X(73)90127-3 |
| Reference:
|
[4] Koplatadze, R.: A note on the oscillation of the solutions of higher order differential inequalities and equations with retarded argument.Russian Differentsial'nye Uravneniya 10 (1974), 1400-1405, 1538. MR 0358026 |
| Reference:
|
[5] Koplatadze, R., Chanturia, T.: Oscillatory properties of differential equations with deviating argument.Russian With Georgian and English summaries. Izdat. Tbilis. Univ., Tbilisi (1977), 115. MR 0492725 |
| Reference:
|
[6] Koplatadze, R.: Some properties of the solutions of nonlinear differential inequalities and equations with retarded argument.Russian Differentsial'nye Uravneniya 12 (1976), 1971-1984. MR 0466843 |
| Reference:
|
[7] Koplatadze, R.: On oscillatory properties of solutions of functional-differential equations.Mem. Differential Equations Math. Phys. 3 (1994), 179 pp. Zbl 0843.34070, MR 1375838 |
| Reference:
|
[8] Koplatadze, R.: On asymptotic behaviour of solutions of functional-differential equations.Equadiff 8 (Bratislava, 1993). Tatra Mt. Math. Publ. 4 (1994), 143-146. Zbl 0809.34081, MR 1298463 |
| Reference:
|
[9] Koplatadze, R.: Quasi-linear functional differential equations with Property A.J. Math. Anal. Appl. 330 (2007), 483-510. MR 2302938, 10.1016/j.jmaa.2006.07.085 |
| Reference:
|
[10] Graef, J., Koplatadze, R., Kvinikadze, G.: Nonlinear functional differential equations with Properties A and B.J. Math. Anal. Appl. 306 (2005), 136-160. Zbl 1069.34088, MR 2132894, 10.1016/j.jmaa.2004.12.034 |
| Reference:
|
[11] Koplatadze, R.: On asymptotic behavior of solutions of Emden-Fowler advanced differential equation.Math. Modeling and Computer Simulation of Material Technologies. Proceedings of the 5-th International Conference Ariel 2 (2008), 731-735. |
| Reference:
|
[12] Koplatadze, R.: On oscillatory properties of solutions of generalized Emden-Fowler type differential equations.Proc. A. Razmadze Math. Inst. 145 (2007), 117-121. Zbl 1154.34323, MR 2387454 |
| Reference:
|
[13] Koplatadze, R.: On asymptotic behavior of solutions of almost linear and essentially nonlinear differential equations.Nonlinear Anal. Theory, Methods and Appl. (accepted). |
| Reference:
|
[14] Gramatikopoulos, M. K., Koplatadze, R., Kvinikadze, G.: Linear functional differential equations with Property A.J. Math. Anal. Appl. 284 (2003), 294-314. MR 1996134, 10.1016/S0022-247X(03)00356-1 |
| . |
