| Title:
|
A remark on Nehari-type oscillation criteria for self-adjoint linear differential equations (English) |
| Author:
|
Došlý, Ondřej |
| Author:
|
Fiedler, Frank |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
447-462 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Oscillation criteria of Nehari-type for the equation $(-1)^n(x^{\alpha}y^{(n)})^{(n)} + q(x)y = 0$, $\alpha\in {\bold R}$, are established. These criteria impose no sign restriction on the function $q(x)$ and generalize some recent results of the second author. (English) |
| Keyword:
|
Nehari-type oscillation criteria |
| Keyword:
|
conjugate points |
| Keyword:
|
self-adjoint equation |
| Keyword:
|
principal solution |
| MSC:
|
34A30 |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 0751.34017 |
| idMR:
|
MR1159793 |
| . |
| Date available:
|
2009-01-08T17:46:04Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118426 |
| . |
| Reference:
|
[1] Coppel W.A.: Disconjugacy.Lectures Notes in Math. No. 220, Springer Verlag, Berlin-Heidelberg, 1971. Zbl 0224.34003, MR 0460785 |
| Reference:
|
[2] Došlý O.: The existence of conjugate points for self-adjoint linear differential equations.Proc. Roy. Soc. Edinburgh 112A, (1989), 73-85. MR 1025455 |
| Reference:
|
[3] Došlý O.: Oscillation criteria for self-adjoint linear differential equations.submitted to Diff. Integral Equations. |
| Reference:
|
[4] Fiedler F.: Hinreichende Oszillationkriterien für gewöhnliche Differentialoperatoren höher Ordnung.Math. Nachr. 96 (1980), 35-48. MR 0600799 |
| Reference:
|
[5] Fiedler F.: Oszillationkriterien vom Nehari-Typ für gewöhnliche Differentialoperatoren vierter and sechster Ordnung.Beiträge Anal. 18 (1981), 113-132. MR 0650144 |
| Reference:
|
[6] Fiedler F.: Oscillation criteria for a class of $2n$-order ordinary differential operators.J. Diff. Equations 42 (1981), 155-185. Zbl 0452.34031, MR 0641646 |
| Reference:
|
[7] Fiedler F.: Oscillation criteria for a special class of $2n$-order ordinary differential equations.Math. Nachr. 131 (1987), 205-218. Zbl 0644.34024, MR 0908812 |
| Reference:
|
[8] Glazman I.M.: Direct Methods of Qualitative Spectral Analysis of Singular Differential operators.Davey, Jerusalem, 1965. Zbl 0143.36505, MR 0190800 |
| Reference:
|
[9] Lewis R.T.: Oscillation and nonoscillation criteria for some self-adjoint even order linear differential operators.Pacific J. Math. 51 (1974), 221-234. Zbl 0281.34027, MR 0350112 |
| Reference:
|
[10] Müller-Pfeiffer E.: Oscillation criteria of Nehari-type for Schrödinger equation.Math. Nachr. 96 (1980), 185-194. MR 0600809 |
| Reference:
|
[11] Nehari Z.: Oscillation criteria for second order linear differential equations.Trans. Amer. Math. Soc. 85 (1957), 428-445. Zbl 0078.07602, MR 0087816 |
| . |
