Geodesic
Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients
Mathematica Bohemica, Tome 124 (1999) no. 1, pp. 87-102

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form \(x(t)-cx(t-r)\)'\pm\(P(t)x(t-\theta)-Q(t)x(t-\delta)\)=0 where $c>0$, $r>0$, $\theta>\delta\geq0$ are constants, and $P$, $Q\in C(\bb R^+\!,\bb R^+)$. 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.
In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form \(x(t)-cx(t-r)\)'\pm\(P(t)x(t-\theta)-Q(t)x(t-\delta)\)=0 where $c>0$, $r>0$, $\theta>\delta\geq0$ are constants, and $P$, $Q\in C(\bb R^+\!,\bb R^+)$. 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.
DOI : 10.21136/MB.1999.125974
Classification : 34K11, 34K15, 34K40
Keywords: neutral differential equations; nonoscillation; oscillation; positive and negative coefficients 
Graef, John R.; Yang, Bo; Zhang, B. G. Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients. Mathematica Bohemica, Tome 124 (1999) no. 1, pp. 87-102. doi: 10.21136/MB.1999.125974
@article{10_21136_MB_1999_125974,
     author = {Graef, John R. and Yang, Bo and Zhang, B. G.},
     title = {Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients},
     journal = {Mathematica Bohemica},
     pages = {87--102},
     year = {1999},
     volume = {124},
     number = {1},
     doi = {10.21136/MB.1999.125974},
     mrnumber = {1687484},
     zbl = {0937.34066},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.125974/}
}
TY  - JOUR
AU  - Graef, John R.
AU  - Yang, Bo
AU  - Zhang, B. G.
TI  - Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients
JO  - Mathematica Bohemica
PY  - 1999
SP  - 87
EP  - 102
VL  - 124
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.125974/
DO  - 10.21136/MB.1999.125974
LA  - en
ID  - 10_21136_MB_1999_125974
ER  - 
%0 Journal Article
%A Graef, John R.
%A Yang, Bo
%A Zhang, B. G.
%T Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients
%J Mathematica Bohemica
%D 1999
%P 87-102
%V 124
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.125974/
%R 10.21136/MB.1999.125974
%G en
%F 10_21136_MB_1999_125974

[1] D. D. Bainov D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay. Adam Hilger, Philadelphia, 1991. | MR

[2] Q. Chuanxi G. Ladas: Linearized oscillation for equations with positive, negative coefficients. Hiroshima Math. J. 20 (1990), 331-340. | DOI | MR

[3] L. H. Erbe Q. Kong B. G. Zhang: Oscillation Theory for Functional Differential Equations. Marcel Dekker, New York, 1994. | MR

[4] I. Györi G. Ladas: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford, 1991. | MR

[5] J. Jaroš T. Kusano: Existence of oscillatory solutions for functional differential equations of neutral type. Acta Math. Univ. Comenian. 60 (1991), 185-194. | MR

[6] G. Ladas C. Qian: Oscillation in differential equations with positive, negative coefficients. Canad. Math. Bull. 33 (1990), 442-451. | DOI | MR

[7] B. S. Lalli B. G. Zhang: Oscillation of first order neutral differential equations. Appl. Anal. 39 (1990), 265-274. | DOI | MR

[8] Yu Jianshe, Wang Zhicheng: Some further results on oscillation of neutral differential equations. Bull. Austral. Math. Soc. 46 (1992), 147-154. | MR | Zbl

[9] Yu Jianshe: On the neutral delay differentia! equation with positive, negative coefficients. Acta. Math. Sinica 34 (1991), 517-523. | MR

[10] B. G. Zhang J. S. Yu: The existence of positive solutions of neutral differential equations. Scientia Sinica 8 (1992), 785-790.

Cité par Sources :