Conjugacy criteria for half-linear differential equations

Simón Peňa

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 1, page 1-11
  • ISSN: 0044-8753

Abstract

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Sufficient conditions on the function c ( t ) ensuring that the half-linear second order differential equation ( | u ' | p - 2 u ' ) ' + c ( t ) | u ( t ) | p - 2 u ( t ) = 0 , 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 .

How to cite

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Peňa, Simón. "Conjugacy criteria for half-linear differential equations." Archivum Mathematicum 035.1 (1999): 1-11. <http://eudml.org/doc/248349>.

@article{Peňa1999,
abstract = {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 $p=2$.},
author = {Peňa, Simón},
journal = {Archivum Mathematicum},
keywords = {half-linear equation; scalar p-Laplacian; conjugate points; conjugacy criteria; half-linear equation; scalar -Laplacian; conjugacy},
language = {eng},
number = {1},
pages = {1-11},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Conjugacy criteria for half-linear differential equations},
url = {http://eudml.org/doc/248349},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Peňa, Simón
TI - Conjugacy criteria for half-linear differential equations
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 1
SP - 1
EP - 11
AB - 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 $p=2$.
LA - eng
KW - half-linear equation; scalar p-Laplacian; conjugate points; conjugacy criteria; half-linear equation; scalar -Laplacian; conjugacy
UR - http://eudml.org/doc/248349
ER -

References

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  1. Conjugacy criteria for second order differential equations, Rocky Mountain, J. Math. 23(1993), 849-861. MR1245450
  2. A half-linear second order differential equation, Colloquia Math. Soc. Janos Bolyai, 30, Qualitative theory of differential equation, Szeged (1979), 153-180. Zbl0511.34006MR0680591
  3. On the oscillation of differential equations with an oscillatory coefficient, Trans. Amer. Math. Soc. 347(1995), 1831-1839. MR1283552
  4. Oscillations of half-linear second order differential equations, Hiroshima Math. J. 25(1995), 585-594. MR1364076
  5. Existence of conjugate points for second and fourth order differential equations, Proc. Roy. Soc. Edinburgh Sect. A 89(1981), 281-291. MR0635764
  6. General relativity and conjugate ordinary differential equations, J. Diff. Equations 30(1978), 165-174. Zbl0362.34023MR0513268

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