| Title:
|
On an oscillation criterion of Hartman, Wintner and Potter (English) |
| Author:
|
Heil, Erhard |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
15 |
| Issue:
|
2 |
| Year:
|
1979 |
| Pages:
|
81-91 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 0378.34026 |
| idMR:
|
MR563141 |
| . |
| Date available:
|
2008-06-06T06:06:10Z |
| Last updated:
|
2012-05-09 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107027 |
| . |
| Reference:
|
[1] Breuer S., Gottlieb D.: Separation of roots and oscillation in ordinary linear differential equations of second order.Proc. Amer. Math. Soc. 29 (1971), 487-493. Zbl 0224.34024, MR 0276545 |
| Reference:
|
[2] Caratheodory C.: Vorlesungen über reelle Funktionen.2. Aufl. Teubner Leipzig 1927. |
| Reference:
|
[3] Etgen G. J., Pawlowski J. F.: Oscillation criteria for second order self adjoint differential systems.Pacific J. Math. 66 (1976) 99-110. Zbl 0355.34017, MR 0440147 |
| Reference:
|
[4] Fite W. B.: Concerning the zeros of the solutions of certain differential equations.Trans. Amer. Math. Soc. 19 (1917), 341-352. MR 1501107 |
| Reference:
|
[5] Gagliardo E.: Sul comportamento asintotico degli integrali dell'equazione differenziale $y" + A(x) y =0$ con $A(x) \geq 0$.Boll. Unione Mat. Ital. (3) 8 (1953), 177-185. MR 0056779 |
| Reference:
|
[6] Guggenheimer H.: Hill equations with coexisting periodic solutions.J. Diff. Equations 5 (1969), 159-166. Zbl 0186.41003, MR 0239193 |
| Reference:
|
[7] Hartman P., Wintner A.: On non-conservative linear oscillators of low frequency.Amer. J. Math. 70 (1948), 529-539. Zbl 0037.19002, MR 0026736 |
| Reference:
|
[8] Kreith K.: Oscillation theory.Lecture Notes in Math. 324, Springer-Verlag Berlin, Heidelberg, New York 1973. Zbl 0258.35001 |
| Reference:
|
[9] Laugwitz D.: Differentialgeometrie in Vektorräumen.Vieweg Braunschweig 1965. Zbl 0139.14904, MR 0182924 |
| Reference:
|
[10] Leighton W.: Principal quadratic functionals and self adjoint second-order differential equations.Proc. Nat. Acad. Sci. 35 (1949) 192-193. Zbl 0032.34603, MR 0030672 |
| Reference:
|
[11] Leighton W.: On self adjoint differential equations of second order.J. London Math. Soc. 27 (1952), 37-47. Zbl 0048.06503, MR 0046506 |
| Reference:
|
[12] Moore R. A.: The behavior of solutions of a linear differential equation of second order.Pacific J. Math. 5 (1955), 125-145. MR 0068690 |
| Reference:
|
[13] Neuman F.: Centroaffine invariants of plane curves in connection with the theory of the second order linear differential equations.Archivum Math. (Brno) 4 (1968), 201-216. Zbl 0218.34007, MR 0267512 |
| Reference:
|
[14] Opial Z.: Sur une critère d'oscillation des integrales de l'equation différentielle $(Q(t) x')' + f(t)x = 0$.Ann. Polon. Math. 6 (1959/1960), 99-104. MR 0104876 |
| Reference:
|
[15] Pfaff R.: Zur Theorie der gewöhnlichen linearen Differentialgleichung zweiter Ordnung mit Distributionskoeffizient.Dissertation Darmstadt 1978. MR 0481259 |
| Reference:
|
[16] Potter R. L.: On self-adjoint differential equations of second order.Pacific J. Math. 3 (1953),. 467-491. Zbl 0051.06502, MR 0056156 |
| Reference:
|
[17] Ráb M.: Kriterien für die Oszillation der Lösungen der Differentialgleichung $[p(x)y']' + q(x)y = 0$.Časopis Pěst. Mat. 84 (1959), 335-370. MR 0114964 |
| Reference:
|
[18] Swanson C. A.: Comparison and oscillation theory of linear differential equations.Academic Press New York, London 1968. Zbl 0191.09904, MR 0463570 |
| Reference:
|
[19] Willet D.: Classification of second order linear differential equations with respect to oscillation.In: Lectures on ordinary differential equations. Ed. R. McKelvey, Academic Press New York, London 1970. MR 0280800 |
| Reference:
|
[20] Wintner A.: A criterion of oscillatory stability.Quarterly Appl. Math. 7 (1949), 115-117. Zbl 0032.34801, MR 0028499 |
| . |
