| Title:
|
On nonoscillation of canonical or noncanonical disconjugate functional equations (English) |
| Author:
|
Singh, Bhagat |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
627-639 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Qualitative comparison of the nonoscillatory behavior of the equations \[ L_ny(t) + H(t,y(t)) = 0 \] and \[ L_ny(t) + H(t,y(g(t))) = 0 \] is sought by way of finding different nonoscillation criteria for the above equations. $L_n$ is a disconjugate operator of the form \[ L_n = \frac{1}{p_n(t)} \frac{\mathrm{d}{}}{\mathrm{d}t} \frac{1}{p_{n-1}(t)} \frac{\mathrm{d}{}}{\mathrm{d}t} \ldots \frac{\mathrm{d}{}}{\mathrm{d}t} \frac{\cdot }{p_0(t)}. \] Both canonical and noncanonical forms of $L_n$ have been studied. (English) |
| Keyword:
|
canonical |
| Keyword:
|
noncanonical |
| Keyword:
|
oscillatory |
| Keyword:
|
nonoscillatory |
| Keyword:
|
principal system |
| MSC:
|
34K11 |
| MSC:
|
34K15 |
| MSC:
|
34K25 |
| MSC:
|
35J30 |
| MSC:
|
35R10 |
| idZBL:
|
Zbl 1079.34545 |
| idMR:
|
MR1777483 |
| . |
| Date available:
|
2009-09-24T10:36:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127598 |
| . |
| Reference:
|
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| Reference:
|
[2] J. Dzurina, J. Ohriska: Asymptotic and oscillatory properties of differential equations with deviating argument.Hiroshima Math. J. 22 (1992), 561–571. MR 1194051, 10.32917/hmj/1206128503 |
| Reference:
|
[3] H. Onose: Oscillatory properties of ordinary differential equations of arbitrary order.J. Differential Equations 7 (1970), 454–458. MR 0257465, 10.1016/0022-0396(70)90093-8 |
| Reference:
|
[4] Ch. G. Philos: Oscillatory and asymptotic behavior of differential equations with deviating arguments.Proc. Roy. Soc. Edinburgh 81 (1978), 195–210. MR 0516413 |
| Reference:
|
[5] Ch. G. Philos, V. A. Staikos: Asymptotic properties of nonoscillatory solutions of differential equations with deviating arguments.Pacific J. Math. 70 (1977), 221–242. MR 0466876, 10.2140/pjm.1977.70.221 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[13] V. A. Staikos, Ch. G. Philos: Nonoscillatory phenomena and damped oscillations.Nonlinear Anal. 2 (1978), 197–210. MR 0512283, 10.1016/0362-546X(78)90066-4 |
| Reference:
|
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| Reference:
|
[15] W. F. Trench: Canonical forms and principal systems in general disconjugate equations.Trans. Amer. Math. Soc. 189 (1974), 319–327. MR 0330632, 10.1090/S0002-9947-1974-0330632-X |
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