Geodesic
Asymptotische Eigenschaften von Lösungen der Differentialgleichung $y''=A(x)\cdot y$ im nichtoszillatorischen Fall
Czechoslovak Mathematical Journal, Tome 10 (1960) no. 4, pp. 501-522
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

DOI : 10.21136/CMJ.1960.100431
Classification : 34C10 
@article{10_21136_CMJ_1960_100431,
     author = {Ma\v{r}{\'\i}k, Jan and R\'ab, Milo\v{s}},
     title = {Asymptotische {Eigenschaften} von {L\"osungen} der {Differentialgleichung} $y''=A(x)\cdot y$ im nichtoszillatorischen {Fall}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {501--522},
     year = {1960},
     volume = {10},
     number = {4},
     doi = {10.21136/CMJ.1960.100431},
     mrnumber = {0138842},
     zbl = {0097.07104},
     language = {de},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1960.100431/}
}
TY  - JOUR
AU  - Mařík, Jan
AU  - Ráb, Miloš
TI  - Asymptotische Eigenschaften von Lösungen der Differentialgleichung $y''=A(x)\cdot y$ im nichtoszillatorischen Fall
JO  - Czechoslovak Mathematical Journal
PY  - 1960
SP  - 501
EP  - 522
VL  - 10
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1960.100431/
DO  - 10.21136/CMJ.1960.100431
LA  - de
ID  - 10_21136_CMJ_1960_100431
ER  - 
%0 Journal Article
%A Mařík, Jan
%A Ráb, Miloš
%T Asymptotische Eigenschaften von Lösungen der Differentialgleichung $y''=A(x)\cdot y$ im nichtoszillatorischen Fall
%J Czechoslovak Mathematical Journal
%D 1960
%P 501-522
%V 10
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1960.100431/
%R 10.21136/CMJ.1960.100431
%G de
%F 10_21136_CMJ_1960_100431
Mařík, Jan; Ráb, Miloš. Asymptotische Eigenschaften von Lösungen der Differentialgleichung $y''=A(x)\cdot y$ im nichtoszillatorischen Fall. Czechoslovak Mathematical Journal, Tome 10 (1960) no. 4, pp. 501-522. doi: 10.21136/CMJ.1960.100431

[1] F. V. Atkinson: Asymptotic formulae for linear oscillations. Proceedings Glasgow Math. Association 3 (1957), 105-111. | DOI | MR | Zbl

[2] R. Bellman: Boundedness of the solutions of second order linear differential equations. Duke Math. J. 22 (1955), 511-513. | MR | Zbl

[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. | DOI | MR

[4] V. Doležal: Asymptotické vzorce pro řeseni diferenciálni rovnice y" + f(t) y = 0. Časopis pro pěst. mat. 83 (1958), 4, 451-465. | MR

[5] P. Hartman: Differential equations with non-oscillatory solutions. Duke Math. J. 15 (1948), 697-709. | DOI | MR

[6] P. Hartman A. Wintner: Asymptotic integrations of linear differential equations. Amer. J. Math. 77 (1955), 45-86. | DOI | MR

[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. | DOI | MR

[8] P. Hartman A. Wintner: Oscillatory and non-oscillatory linear differential equations. Amer. J. Math. 71 (1949), 627-649. | DOI | MR

[9] E. Hille: Non oscillation theorems. Trans. Amer. Math. Soc. 64 (1948), 234-252. | DOI | MR | Zbl

[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.

[11] M. Ráb: Asymptotische Eigenschaften der Lösungen der Differentialgleichung y" + A(x) y = 0. Чех. мат. журнал 8 (83) (1958), 513-519. | MR

[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.

[13] A. Wintner: Asymptotic integrations of the adiabatic oscillator in its hyperbolic range. Duke Math. J. 15 (1948), 55-67. | MR | Zbl

[14] A. Wintner: On the normalization of characteristic differentials in continuous spectra. Physical Review. 72 (1947), 516-517. | DOI | MR | Zbl

[15] M. Zlámal: Über asymptotische Eigenschaften der Lösungen der linearen Differentialgleichung zweiter Ordnung. Чех. мат. журнал 6 (81), 1956, 75-93. | MR

[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.

Cité par Sources :