Nonoscillation and asymptotic behaviour for third order nonlinear differential equations

Aydın Tiryaki; A. Okay Çelebi

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 4, page 677-685
  • ISSN: 0011-4642

Abstract

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In this paper we consider the equation y ' ' ' + q ( t ) y ' α + p ( t ) h ( y ) = 0 , where p , q are real valued continuous functions on [ 0 , ∞ ) such that q ( t ) ≥ 0 , p ( t ) ≥ 0 and h ( y ) is continuous in ( - ∞ , ∞ ) such that h ( y ) y > 0 for y ≠ 0 . We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.

How to cite

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Tiryaki, Aydın, and Çelebi, A. Okay. "Nonoscillation and asymptotic behaviour for third order nonlinear differential equations." Czechoslovak Mathematical Journal 48.4 (1998): 677-685. <http://eudml.org/doc/30446>.

@article{Tiryaki1998,
abstract = {In this paper we consider the equation \[y^\{\prime \prime \prime \} + q(t)\{y^\{\prime \}\}^\{\alpha \} + p(t) h(y) =0,\] where $p,q$ are real valued continuous functions on $[0,\infty )$ such that $q(t) \ge 0$, $p(t) \ge 0$ and $h(y)$ is continuous in $(-\infty ,\infty )$ such that $h(y)y>0$ for $y \ne 0$. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.},
author = {Tiryaki, Aydın, Çelebi, A. Okay},
journal = {Czechoslovak Mathematical Journal},
keywords = {Third order nonlinear differential equations; nonoscillatory solutions; asymptotic properties of solutions; third-order nonlinear differential equations; nonoscillatory solutions; asymptotic properties of solutions},
language = {eng},
number = {4},
pages = {677-685},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonoscillation and asymptotic behaviour for third order nonlinear differential equations},
url = {http://eudml.org/doc/30446},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Tiryaki, Aydın
AU - Çelebi, A. Okay
TI - Nonoscillation and asymptotic behaviour for third order nonlinear differential equations
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 4
SP - 677
EP - 685
AB - In this paper we consider the equation \[y^{\prime \prime \prime } + q(t){y^{\prime }}^{\alpha } + p(t) h(y) =0,\] where $p,q$ are real valued continuous functions on $[0,\infty )$ such that $q(t) \ge 0$, $p(t) \ge 0$ and $h(y)$ is continuous in $(-\infty ,\infty )$ such that $h(y)y>0$ for $y \ne 0$. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.
LA - eng
KW - Third order nonlinear differential equations; nonoscillatory solutions; asymptotic properties of solutions; third-order nonlinear differential equations; nonoscillatory solutions; asymptotic properties of solutions
UR - http://eudml.org/doc/30446
ER -

References

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