| Title:
|
On oscillatory solutions of fourth order ordinary differential equations (English) |
| Author:
|
Palumbíny, Oleg |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
779-790 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the oscillation of a differential equation $L_4y+P(t)L_2y+Q(t)y\equiv 0$ as well as with the structure of its fundamental system of solutions. (English) |
| Keyword:
|
linear differential equation |
| Keyword:
|
quasi-derivative |
| Keyword:
|
monotone solution |
| Keyword:
|
Kneser solution |
| Keyword:
|
oscillatory solution |
| MSC:
|
34A25 |
| MSC:
|
34A30 |
| MSC:
|
34C10 |
| MSC:
|
34D05 |
| idZBL:
|
Zbl 1015.34018 |
| idMR:
|
MR1746703 |
| . |
| Date available:
|
2009-09-24T10:27:30Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127527 |
| . |
| Reference:
|
[G] Gera, M.: Nichtoszillatorische und oszillatorische Differentialgleichungen dritter Ordnung.Čas. Pěst. Mat., 96 (1971), 278–293. Zbl 0222.34034, MR 0291556 |
| Reference:
|
[Gr] Greguš, M.: Oszillatorische Eigenschaften der Lösungen der linearen Differentialgleichung dritter Ordnung $y^{\prime \prime \prime } + 2Ay^{\prime } + (A^{\prime } + b)y = 0$, wo $A = A(x) \le 0$ ist.Czechoslovak Math. J., 9(84) (1959), 416–428. MR 0111888 |
| Reference:
|
[H] Heidel, J. W.: Qualitative behavior of solutions of a third order nonlinear differential equation.Pac. J. Math., 27 (1968), 507–526. Zbl 0172.11703, MR 0240389, 10.2140/pjm.1968.27.507 |
| Reference:
|
[LN] Leighton, W. and Nehari, Z.: On the oscillation of solutions of self-adjoint linear differential equations of the fourth order.Trans. Amer. Math. Soc., 89 (1958), 325–377. MR 0102639, 10.1090/S0002-9947-1958-0102639-X |
| Reference:
|
[R] Regenda, J.: Oscillation criteria for fourth-order linear differential equations.Math. Slovaca, 29 (1979), 3–16. Zbl 0408.34032, MR 0561771 |
| Reference:
|
[Ro] Rovder, J.: Oscillation criteria for third-order linear differential equations.Mat. Čas., 25 (1975), 231–244. Zbl 0309.34028, MR 0412521 |
| Reference:
|
[S] Shair, A.: On the oscillation of solutions of a class of linear fourth order differential equations.Pac. J. Math., 34 (1970), 289–299. MR 0268455, 10.2140/pjm.1970.34.289 |
| Reference:
|
[Š] Šoltés, V.: Oscillatory properties of solutions of a fourth-order nonlinear differential equation.Math. Slovaca, 29 (1979), 73–82. MR 0561780 |
| Reference:
|
[Šv] Švec, M.: Einige asymptotische und oszillatorische Eigenschaften der Differentialgleichung $y^{\prime \prime \prime } + A(x)y^{\prime } + B(x)y = 0$.Czechoslovak Math. J., 15 (1965), 378–393. Zbl 0143.11202, MR 0185187 |
| Reference:
|
[TP] Tóthová, M. and Palumbíny, O.: On monotone solutions of the fourth order ordinary differential equations.Czechoslovak Math. J., 45(120) (1995), 737–746. MR 1354930 |
| . |
