Title:
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Conjugacy criteria for half-linear differential equations (English) |
Author:
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Peňa, Simón |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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35 |
Issue:
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1 |
Year:
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1999 |
Pages:
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1-11 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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Sufficient conditions on the function $c(t)$ ensuring that the half-linear second order differential equation \[ (|u^\prime |^{p-2} u^\prime )^\prime + c(t)|u(t)|^{p-2} u(t)=0\,, \quad \quad p>1 \] possesses a nontrivial solution having at least two zeros in a given interval are obtained. These conditions extend some recently proved conjugacy criteria for linear equations which correspond to the case $p=2$. (English) |
Keyword:
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half-linear equation |
Keyword:
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scalar p-Laplacian |
Keyword:
|
conjugate points |
Keyword:
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conjugacy criteria |
MSC:
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34C10 |
idZBL:
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Zbl 1054.34055 |
idMR:
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MR1684518 |
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Date available:
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2008-06-06T22:22:24Z |
Last updated:
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2012-05-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/107680 |
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Reference:
|
[1] Došlý, O.: Conjugacy criteria for second order differential equations.Rocky Mountain, J. Math. 23(1993), 849-861. MR 1245450 |
Reference:
|
[2] Elbert, Á.: A half-linear second order differential equation.Colloquia Math. Soc. Janos Bolyai, 30, Qualitative theory of differential equation, Szeged (1979), 153-180. Zbl 0511.34006, MR 0680591 |
Reference:
|
[3] Harris, B. J., Kong, Q.: On the oscillation of differential equations with an oscillatory coefficient.Trans. Amer. Math. Soc. 347(1995), 1831-1839. MR 1283552 |
Reference:
|
[4] Li, H. J., Yeh, C. Ch.: Oscillations of half-linear second order differential equations.Hiroshima Math. J. 25(1995), 585-594. MR 1364076 |
Reference:
|
[5] Müller-Pfeiffer, E.: Existence of conjugate points for second and fourth order differential equations.Proc. Roy. Soc. Edinburgh Sect. A 89(1981), 281-291. MR 0635764 |
Reference:
|
[6] Tipler, F. J.: General relativity and conjugate ordinary differential equations.J. Diff. Equations 30(1978), 165-174. Zbl 0362.34023, MR 0513268 |
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