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Title: Conjugacy criteria for half-linear differential equations (English)
Author: Peňa, Simón
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 35
Issue: 1
Year: 1999
Pages: 1-11
Summary lang: English
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Category: math
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Summary: 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: half-linear equation
Keyword: scalar p-Laplacian
Keyword: conjugate points
Keyword: conjugacy criteria
MSC: 34C10
idZBL: Zbl 1054.34055
idMR: MR1684518
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Date available: 2008-06-06T22:22:24Z
Last updated: 2012-05-10
Stable URL: 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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