# Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients

Mathematica Bohemica (1999)

• Volume: 124, Issue: 1, page 87-102
• ISSN: 0862-7959

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## Abstract

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In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form $x\left(t\right)-cx\left(t-r\right)$$P\left(t\right)x\left(t-\theta \right)-Q\left(t\right)x\left(t-\delta \right)$=0 where $c>0$, $r>0$, $\theta >\delta \ge 0$ are constants, and $P$, $Q\in C\left({ℝ}^{+}\phantom{\rule{-0.166667em}{0ex}},{ℝ}^{+}\right)$. We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient conditions for the existence of bounded and unbounded oscillatory solutions.

## How to cite

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Graef, John R., Yang, Bo, and Zhang, Bing Gen. "Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients." Mathematica Bohemica 124.1 (1999): 87-102. <http://eudml.org/doc/248321>.

@article{Graef1999,
abstract = {In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form $x(t)-cx(t-r)$’$P(t)x(t-\theta )-Q(t)x(t-\delta )$=0 where $c>0$, $r>0$, $\theta >\delta \ge 0$ are constants, and $P$, $Q\in C(\mathbb \{R\}^+\!,\mathbb \{R\}^+)$. We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient conditions for the existence of bounded and unbounded oscillatory solutions.},
author = {Graef, John R., Yang, Bo, Zhang, Bing Gen},
journal = {Mathematica Bohemica},
keywords = {neutral differential equations; nonoscillation; oscillation; positive and negative coefficients; neutral differential equations; nonoscillation; oscillation; positive and negative coefficients},
language = {eng},
number = {1},
pages = {87-102},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients},
url = {http://eudml.org/doc/248321},
volume = {124},
year = {1999},
}

TY - JOUR
AU - Graef, John R.
AU - Yang, Bo
AU - Zhang, Bing Gen
TI - Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 1
SP - 87
EP - 102
AB - In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form $x(t)-cx(t-r)$’$P(t)x(t-\theta )-Q(t)x(t-\delta )$=0 where $c>0$, $r>0$, $\theta >\delta \ge 0$ are constants, and $P$, $Q\in C(\mathbb {R}^+\!,\mathbb {R}^+)$. We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient conditions for the existence of bounded and unbounded oscillatory solutions.
LA - eng
KW - neutral differential equations; nonoscillation; oscillation; positive and negative coefficients; neutral differential equations; nonoscillation; oscillation; positive and negative coefficients
UR - http://eudml.org/doc/248321
ER -

## References

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8. Yu Jianshe, Wang Zhicheng, Some further results on oscillation of neutral differential equations, Bull. Austral. Math. Soc. 46 (1992), 147-154. (1992) Zbl0729.34051MR1170449
9. Yu Jianshe, On the neutral delay differentia! equation with positive, negative coefficients, Acta. Math. Sinica 34 (1991), 517-523. (1991) MR1152147
10. B. G. Zhang J. S. Yu, The existence of positive solutions of neutral differential equations, Scientia Sinica 8 (1992), 785-790. (1992)

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