Oscillation criteria for fourth order half-linear differential equations

Jaroslav Jaroš; Kusano Takaŝi; Tomoyuki Tanigawa

Archivum Mathematicum (2020)

  • Volume: 056, Issue: 2, page 115-125
  • ISSN: 0044-8753

Abstract

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Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form ( | y ' ' | α sgn y ' ' ) ' ' + q ( t ) | y | α sgn y = 0 , t ≥ a > 0 , A where α > 0 is a constant and q ( t ) is positive continuous function on [ a , ∞ ) , are given in terms of an increasing continuously differentiable function ω ( t ) from [ a , ∞ ) to ( 0 , ∞ ) which satisfies ∫ a ∞ 1 / ( t ω ( t ) ) d t < ∞ .

How to cite

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Jaroš, Jaroslav, Takaŝi, Kusano, and Tanigawa, Tomoyuki. "Oscillation criteria for fourth order half-linear differential equations." Archivum Mathematicum 056.2 (2020): 115-125. <http://eudml.org/doc/297002>.

@article{Jaroš2020,
abstract = {Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form \begin\{equation*\} \big (|y^\{\prime \prime \}|^\alpha \{\rm sgn\ \} y^\{\prime \prime \}\big )^\{\prime \prime \} + q(t)|y|^\alpha \{\rm sgn\}\ y = 0, \quad t \ge a > 0, A \end\{equation*\} where $\alpha > 0$ is a constant and $q(t)$ is positive continuous function on $[a,\infty )$, are given in terms of an increasing continuously differentiable function $\omega (t)$ from $[a,\infty )$ to $(0,\infty )$ which satisfies $\int _a^\infty 1/(t\omega (t))\,dt < \infty $.},
author = {Jaroš, Jaroslav, Takaŝi, Kusano, Tanigawa, Tomoyuki},
journal = {Archivum Mathematicum},
keywords = {half-linear differential equation; oscillatory solutions},
language = {eng},
number = {2},
pages = {115-125},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillation criteria for fourth order half-linear differential equations},
url = {http://eudml.org/doc/297002},
volume = {056},
year = {2020},
}

TY - JOUR
AU - Jaroš, Jaroslav
AU - Takaŝi, Kusano
AU - Tanigawa, Tomoyuki
TI - Oscillation criteria for fourth order half-linear differential equations
JO - Archivum Mathematicum
PY - 2020
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 056
IS - 2
SP - 115
EP - 125
AB - Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form \begin{equation*} \big (|y^{\prime \prime }|^\alpha {\rm sgn\ } y^{\prime \prime }\big )^{\prime \prime } + q(t)|y|^\alpha {\rm sgn}\ y = 0, \quad t \ge a > 0, A \end{equation*} where $\alpha > 0$ is a constant and $q(t)$ is positive continuous function on $[a,\infty )$, are given in terms of an increasing continuously differentiable function $\omega (t)$ from $[a,\infty )$ to $(0,\infty )$ which satisfies $\int _a^\infty 1/(t\omega (t))\,dt < \infty $.
LA - eng
KW - half-linear differential equation; oscillatory solutions
UR - http://eudml.org/doc/297002
ER -

References

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