An oscillatory half-linear differential equation

Árpád Elbert; Takaŝi Kusano; Tomoyuki Tanigawa

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 4, page 355-361
  • ISSN: 0044-8753

Abstract

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A second-order half-linear ordinary differential equation of the type ( | y ' | α - 1 y ' ) ' + α q ( t ) | y | α - 1 y = 0 ( 1 ) is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.

How to cite

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Elbert, Árpád, Kusano, Takaŝi, and Tanigawa, Tomoyuki. "An oscillatory half-linear differential equation." Archivum Mathematicum 033.4 (1997): 355-361. <http://eudml.org/doc/248023>.

@article{Elbert1997,
abstract = {A second-order half-linear ordinary differential equation of the type \[(|y^\{\prime \}|^\{\alpha -1\}y^\{\prime \})^\{\prime \}+\alpha q(t)|y|^\{\alpha -1\}y=0 \qquad \{\{\rm (1)\}\}\] is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.},
author = {Elbert, Árpád, Kusano, Takaŝi, Tanigawa, Tomoyuki},
journal = {Archivum Mathematicum},
keywords = {half-linear differential equations},
language = {eng},
number = {4},
pages = {355-361},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An oscillatory half-linear differential equation},
url = {http://eudml.org/doc/248023},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Elbert, Árpád
AU - Kusano, Takaŝi
AU - Tanigawa, Tomoyuki
TI - An oscillatory half-linear differential equation
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 4
SP - 355
EP - 361
AB - A second-order half-linear ordinary differential equation of the type \[(|y^{\prime }|^{\alpha -1}y^{\prime })^{\prime }+\alpha q(t)|y|^{\alpha -1}y=0 \qquad {{\rm (1)}}\] is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.
LA - eng
KW - half-linear differential equations
UR - http://eudml.org/doc/248023
ER -

References

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  1. Elbert Á., A half-linear second order differential equation, Colloquia Math. Soc. János Bolyai 34: Qualitative Theory of Differential Equation, Szeged (1979), 153 - 180. (1979) MR0680591
  2. Elbert Á., Oscillation and nonoscillation theorems for some non-linear ordinary differential equations, Lecture Notes in Mathematics (Springer), Vol. 956 (1982), 187 - 212. (1982) MR0693113
  3. E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, Reading, Massachusetts (1969). (1969) Zbl0179.40301MR0249698
  4. Li H. J., Yeh C. C., Sturmian comparison theorem for half-linear second order differential equations, Proc. Royal Soc. Edinburgh 125A (1995), 1193 - 1204. (1995) Zbl0873.34020MR1362999
  5. Piros M., On the solutions of a half-Linear differential equation, Studia Sci. Math. Hungar., 19 (1984), 193 - 211. (1984) Zbl0638.34024MR0874484

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