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

John R. Graef; Bo Yang; Bing Gen Zhang

Mathematica Bohemica (1999)

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

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topGraef, 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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