| Title:
|
Minimal and maximal solutions of fourth order iterated differential equations with singular nonlinearity (English) |
| Author:
|
Rostás, Kristína |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
23-33 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we are concerned with sufficient conditions for the existence of minimal and maximal solutions of differential equations of the form
\[ L_{4}y+f(t,y)=0\,, \]
where $L_{4}y$ is the iterated linear differential operator of order $4$ and $f\colon [a,\infty )\times (0,\infty )\rightarrow (0,\infty )$ is a continuous function. (English) |
| Keyword:
|
iterated differential equations |
| Keyword:
|
maximal and minimal solutions |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1240.34181 |
| idMR:
|
MR2813544 |
| . |
| Date available:
|
2011-05-23T12:15:30Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141507 |
| . |
| Reference:
|
[1] Barret, J. H.: Oscillation theory of ordinary linear differential equations.Adv. Math. 3 (1969), 415–509. MR 0257462, 10.1016/0001-8708(69)90008-5 |
| Reference:
|
[2] Fink, A. M., Kusano, T.: Nonoscillation theorems for differential equations with general deviating arguments.Lecture Notes in Math. 1032 (1983), 224–239. Zbl 0531.34052, MR 0742641, 10.1007/BFb0076799 |
| Reference:
|
[3] Kusano, T., Swanson, C. A.: Asymptotic properties of semilinear elliptic equations.Funkcial. Ekvac. 26 (1983), 115–129. Zbl 0536.35024, MR 0736896 |
| Reference:
|
[4] Kusano, T., Swanson, C. A.: Asymptotic theory of singular semilinear elliptic equations.Canad. Math. Bull. 27 (1984), 223–232. Zbl 0589.35046, MR 0740418, 10.4153/CMB-1984-032-1 |
| Reference:
|
[5] Neuman, F.: Oscillatory behavior of iterative linear ordinary differential equations depends on their order.Arch. Math. (Brno) 22 (4) (1986), 187–192. Zbl 0608.34036, MR 0868533 |
| Reference:
|
[6] Pólya, G.: On the mean-value theorem corresponding to a given linear homogeneous differential equations.Trans. Amer. Math. Soc. 24 (1922), 312–324. MR 1501228, 10.2307/1988819 |
| . |
