| Title:
|
Oscillation and nonoscillation of Emden-Fowler type equations of second order (English) |
| Author:
|
Lomtatidze, A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
181-193 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Oscillation and nonoscillation criteria are established for the equation $$u''+p(t)|u|^{\alpha}|u'|^{1-\alpha}\operatorname{sgn} u=0,$$ where $\alpha\in ]0,1]$, and $p:[0,+\infty[\to [0,+\infty[$ is a locally summable function. (English) |
| Keyword:
|
Edmen-Fowler type equation of second order |
| Keyword:
|
oscillatory and nonoscillatory solutions |
| Keyword:
|
oscillatory and nonoscillatory equations |
| MSC:
|
34C10 |
| MSC:
|
34C15 |
| idZBL:
|
Zbl 0908.34023 |
| idMR:
|
MR1421855 |
| . |
| Date available:
|
2008-06-06T21:31:02Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107573 |
| . |
| Reference:
|
[1] Fite W. B.: Concerning the zeros of the solutions of certain differential equations.Trans. Amer. Math. Soc., vol. 19 (1917), pp. 341–352. MR 1501107 |
| Reference:
|
[2] Hille E.: Nonoscillation theorems.Trans. Amer. Math. Soc., vol. 64 (1948), pp. 234–252. MR 0027925 |
| Reference:
|
[3] Del Pino M., Elgueta M., Manasevich R.: Generalized Hartman’s oscillation result for $(|x^{\prime }|^{p-2}x^{\prime })^{\prime }+c(t)|x|^{p-2}=0, p>1.$.Houston Journal of Math., vol. 17 , No 1, (1991) pp. 63–70. Zbl 0733.34039, MR 1107187 |
| Reference:
|
[4] Lomtatidze A.: Oscillation and nonoscillation criteria for second order linear differential equation.Georgian Math. J., vol. 3, No. 2, (1997) pp. 129-138. MR 1439591 |
| Reference:
|
[5] Kiguradze I.T., Shekhter B. L.: Singular boundary value problems for second-order differential equations.in: “Current Problems in Mathematics: Newest Results”, Vol. 3, pp. 3–103, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuzn. Inst. Nauchn. i Tekhn. Inform., Moscow, 1987. [in Russian] MR 0925830 |
| . |
