| Title:
|
Asymptotische Eigenschaften von Lösungen der Differentialgleichung $y''=A(x)\cdot y$ im nichtoszillatorischen Fall (German) |
| Title:
|
Asymptotic properties of solutions of the differential equation $y''=A(x)\cdot y$ in the non-oscilatory case (English) |
| Author:
|
Mařík, Jan |
| Author:
|
Ráb, Miloš |
| Language:
|
German |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
10 |
| Issue:
|
4 |
| Year:
|
1960 |
| Pages:
|
501-522 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 0097.07104 |
| idMR:
|
MR0138842 |
| DOI:
|
10.21136/CMJ.1960.100431 |
| . |
| Date available:
|
2008-06-09T13:08:38Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/100431 |
| . |
| Reference:
|
[1] F. V. Atkinson: Asymptotic formulae for linear oscillations.Proceedings Glasgow Math. Association 3 (1957), 105-111. Zbl 0085.07004, MR 0118886, 10.1017/S2040618500033542 |
| Reference:
|
[2] R. Bellman: Boundedness of the solutions of second order linear differential equations.Duke Math. J. 22 (1955), 511-513. Zbl 0066.33403, MR 0075376 |
| Reference:
|
[3] M. Bôcher: On regular singular points of linear differential equations of the second order whose coefficients are not necessarily analytic.Trans. Amer. Math. Soc. 1 (1900), 40-52. MR 1500523, 10.2307/1986402 |
| Reference:
|
[4] V. Doležal: Asymptotické vzorce pro řeseni diferenciálni rovnice y" + f(t) y = 0.Časopis pro pěst. mat. 83 (1958), 4, 451-465. MR 0101943 |
| Reference:
|
[5] P. Hartman: Differential equations with non-oscillatory solutions.Duke Math. J. 15 (1948), 697-709. MR 0027927, 10.1215/S0012-7094-48-01559-2 |
| Reference:
|
[6] P. Hartman A. Wintner: Asymptotic integrations of linear differential equations.Amer. J. Math. 77 (1955), 45-86. MR 0066520, 10.2307/2372422 |
| Reference:
|
[7] P. Hartman A. Wintner: On the assignment of asymptotic values for the solutions of linear differential equations of second order.Amer. J. Math. 77 (1955), 475-483. MR 0070798, 10.2307/2372635 |
| Reference:
|
[8] P. Hartman A. Wintner: Oscillatory and non-oscillatory linear differential equations.Amer. J. Math. 71 (1949), 627-649. MR 0031158, 10.2307/2372355 |
| Reference:
|
[9] E. Hille: Non oscillation theorems.Trans. Amer. Math. Soc. 64 (1948), 234-252. Zbl 0031.35402, MR 0027925, 10.1090/S0002-9947-1948-0027925-7 |
| Reference:
|
[10] Л. Д. Николенко: Об одном достаточном условии неколебательности решений уравнения у" + A(х) у = 0.Докл. Акад. наук СССР 110 (1956), 6, 929-931. |
| Reference:
|
[11] M. Ráb: Asymptotische Eigenschaften der Lösungen der Differentialgleichung y" + A(x) y = 0.Чех. мат. журнал 8 (83) (1958), 513-519. MR 0103313 |
| Reference:
|
[12] M. Ráb: Poznámka k otázce o oscilačních vlastnostech řešení diferenciálni rovnice y" + A(x) y = 0.Časopis pro pěst. mat. 82 (1957), 342-348. |
| Reference:
|
[13] A. Wintner: Asymptotic integrations of the adiabatic oscillator in its hyperbolic range.Duke Math. J. 15 (1948), 55-67. Zbl 0034.35501, MR 0024537 |
| Reference:
|
[14] A. Wintner: On the normalization of characteristic differentials in continuous spectra.Physical Review. 72 (1947), 516-517. Zbl 0029.29303, MR 0022004, 10.1103/PhysRev.72.516 |
| Reference:
|
[15] M. Zlámal: Über asymptotische Eigenschaften der Lösungen der linearen Differentialgleichung zweiter Ordnung.Чех. мат. журнал 6 (81), 1956, 75-93. MR 0080215 |
| Reference:
|
[16] A. Halanay: Comportarea asimptoticä a soluţiilor ecuaţiitor de ordinul al doilea de tip neoscilator.Comunicärile Acad. Rep. pop. Romîne 9 (1959), 11, 1121-1128. |
| . |
