| Title:
|
A remark on power comparison theorem for half-linear differential equations (English) |
| Author:
|
Bognár, Gabriella |
| Author:
|
Došlý, Ondřej |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
187-195 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the half-linear second order differential equation which is viewed as a perturbation of the so-called Riemann-Weber half-linear differential equation. We present a comparison theorem with respect to the power of the half-linearity in the equation under consideration. Our research is motivated by the recent results published by J. Sugie, N. Yamaoka, Acta Math. Hungar. 111 (2006), 165–179. (English) |
| Keyword:
|
Riemann-Weber half-linear equation |
| Keyword:
|
Riccati technique |
| Keyword:
|
power comparison theorem |
| Keyword:
|
perturbation principle |
| Keyword:
|
principal solution |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1199.34168 |
| idMR:
|
MR2428314 |
| DOI:
|
10.21136/MB.2008.134060 |
| . |
| Date available:
|
2009-09-24T22:36:11Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134060 |
| . |
| Reference:
|
[1] R. P. Agarwal, S. R. Grace, D. O’Regan: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations.Kluwer Academic Publishers, Dordrecht, 2002. MR 2091751 |
| Reference:
|
[2] O. Došlý: Perturbations of the half-linear Euler-Weber type differential equation.J. Math. Anal. Appl. 323 (2006), 426–440. Zbl 1107.34030, MR 2262216, 10.1016/j.jmaa.2005.10.051 |
| Reference:
|
[3] O. Došlý, A. Lomtatidze: Oscillation and nonoscillation criteria for half-linear second order differential equations.Hiroshima Math. J. 36 (2006), 203–219. MR 2259737, 10.32917/hmj/1166642300 |
| Reference:
|
[4] O. Došlý, P. Řehák: Half-Linear Differential Equations.North-Holland Mathematics Studies 202, Elsevier, Amsterdam, 2005. MR 2158903 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] J. D. Mirzov: On some analogs of Sturm’s and Kneser’s theorem for nonlinear systems.J. Math. Anal. Appl. 53 (1976), 418–425. MR 0402184, 10.1016/0022-247X(76)90120-7 |
| Reference:
|
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| Reference:
|
[11] P. Řehák: On certain comparison theorems for half-linear dynamic equations on time scales.Abstr. Appl. Anal. 7 (2004), 551–564. Zbl 1106.34019, MR 2084935 |
| Reference:
|
[12] J. Sugie, N. Yamaoka: Growth conditions and oscillation of nonlinear differential equations with $p$-Laplacian.J. Math. Anal. Appl. 305 (2005), 18–34. MR 2132886 |
| Reference:
|
[13] J. Sugie, N. Yamaoka: Comparison theorems for oscillation of second-order half-linear differential equations.Acta Math. Hungar. 111 (2006), 165–179. MR 2188979, 10.1007/s10474-006-0029-5 |
| . |
