| Title:
             | 
Oscillation and nonoscillation of neutral differential equations with positive and negative coefficients (English) | 
| Author:
             | 
Luo, Zhiguo | 
| Author:
             | 
Shen, Jianhua | 
| Language:
             | 
English | 
| Journal:
             | 
Czechoslovak Mathematical Journal | 
| ISSN:
             | 
0011-4642 (print) | 
| ISSN:
             | 
1572-9141 (online) | 
| Volume:
             | 
54 | 
| Issue:
             | 
1 | 
| Year:
             | 
2004 | 
| Pages:
             | 
79-93 | 
| Summary lang:
             | 
English | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
In this paper, oscillattion and nonoscillation criteria are established for neutral differential equations with positive and negative coefficients. Our criteria improve and extend many results known in the literature. (English) | 
| Keyword:
             | 
oscillation | 
| Keyword:
             | 
neutral differential equations | 
| Keyword:
             | 
positive and negative coefficients | 
| MSC:
             | 
34C10 | 
| MSC:
             | 
34K11 | 
| MSC:
             | 
34K15 | 
| MSC:
             | 
34K40 | 
| idZBL:
             | 
Zbl 1057.34079 | 
| idMR:
             | 
MR2040221 | 
| . | 
| Date available:
             | 
2009-09-24T11:09:54Z | 
| Last updated:
             | 
2020-07-03 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/127866 | 
| . | 
| Reference:
             | 
[1] T. A.  Chanturia: Integral criteria for the oscillation of higher order differential equations.Differencialnye Uravnenija 16 (1980), 470–482. | 
| Reference:
             | 
[2] Q. Chuanxi and G.  Ladas: Oscillation in differential equations with positive and negative coefficients.Canad. Math. Bull. 33 (1990), 442–450. MR 1091349, 10.4153/CMB-1990-072-x | 
| Reference:
             | 
[3] El. M.  Elabbasy, A. S.  Hegazi and S. H.  Saker: Oscillation of solutions to delay differential equations with positive and negative coefficients.Electron. J. Differential Equations 13 (2000), 1–13. MR 1745042 | 
| Reference:
             | 
[4] L. H.  Erbe, Q.  Kong and B. G.  Zhang: Oscillation Theory for Functional Differential Equations.Marcel Dekker, New York, 1995. MR 1309905 | 
| Reference:
             | 
[5] K.  Farrell, E. A.  Grove and G.  Ladas: Neutral delay differential equations with positive and negative coefficients.Appl. Anal. 27 (1988), 181–197. MR 0922777, 10.1080/00036818808839732 | 
| Reference:
             | 
[6] I.  Gyori and G.  Ladas: Oscillation Theory of Delay Differential Equations with Applications.Clarendon Press, Oxford, 1991. MR 1168471 | 
| Reference:
             | 
[7] E.  Hille: Non-oscillation theorems.Trans. Amer. Math. Soc. 64 (1948), 234–252. Zbl 0031.35402, MR 0027925, 10.1090/S0002-9947-1948-0027925-7 | 
| Reference:
             | 
[8] B.  Li: Oscillation of first order delay differential equations.Proc. Amer. Math. Soc. 124 (1996), 3729–3737. Zbl 0865.34057, MR 1363175, 10.1090/S0002-9939-96-03674-X | 
| Reference:
             | 
[9] S. G.  Ruan: Oscillation for first order neutral differential equations with positive and negative coefficients.Bull. Austral. Math. Soc. 43 (1991), 147–152. MR 1086728, 10.1017/S0004972700028872 | 
| Reference:
             | 
[10] J. H.  Shen and Z. C.  Wang: Oscillation and nonoscillation for a class of nonlinear neutral differential equations.Differential Equations Dynam. Systems 4 (1994), 347–360. MR 1386279 | 
| Reference:
             | 
[11] X. H.  Tang and J. H.  Shen: Oscillation and existence of positive solution in a class of higher order neutral differential equations.J.  Math. Anal. Appl. 213 (1997), 662–680. MR 1470876, 10.1006/jmaa.1997.5567 | 
| Reference:
             | 
[12] X. H. Tang and J. S.  Yu: On the positive solutions of a kind of neutral differential equations with positive and negative coefficients.Acta Math. Sinica 42 (1999), 795–802. MR 1766655 | 
| Reference:
             | 
[13] J. S.  Yu and Z. C.  Wang: Some further results on oscillation of neutral differential equations.Bull. Austral. Math. Soc. 46 (1992), 149–157. MR 1170449, 10.1017/S0004972700011758 | 
| Reference:
             | 
[14] J. S.  Yu and J. R.  Yan: Oscillation in first order neutral differential equations with “integrally small” coefficients.J.  Math. Anal. Appl. 187 (1994), 361–370. MR 1297030, 10.1006/jmaa.1994.1362 | 
| Reference:
             | 
[15] B. G.  Zhang and B.  Yang: New approach of studying the oscillation of neutral differential equations.Funkcial. Ekvac. 41 (1998), 79–89. MR 1627357 | 
| Reference:
             | 
[16] B. G.  Zhang and J. S.  Yu: Oscillation and nonoscillation for neutral differential equations.J.  Math. Anal. Appl. 172 (1993), 11–23. MR 1199490, 10.1006/jmaa.1993.1002 | 
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