- Research Article
- Open access
- Published:
Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments
Journal of Inequalities and Applications volume 2007, Article number: 098423 (2007)
Abstract
We derive oscillation criteria for general-type neutral differential equations,
, where
,
,
,
,
,
and
are real numbers, the functions
and
are nondecreasing in
for each fixed
, and
is periodic and continuous with respect to
for each fixed
. In certain special cases, the results obtained generalize and improve some existing ones in the literature.
References
Hale J: Theory of Functional Differential Equations. 2nd edition. Springer, New York, NY, USA; 1977:x+365.
Agarwal RP, Grace SR, O'Regan D: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic Publishers, Dordrecht, The Netherlands; 2000:viii+337.
Agarwal RP, Grace SR: Oscillation theorems for certain neutral functional-differential equations. Computers & Mathematics with Applications 1999,38(11–12):1–11. 10.1016/S0898-1221(99)00280-1
BaÄnov DD, Mishev DP: Oscillation Theory for Neutral Differential Equations with Delay. IOP, Bristol, UK; 1992.
Candan T, Dahiya RS: Oscillation behavior ofth order neutral differential equations with continuous delay. Journal of Mathematical Analysis and Applications 2004,290(1):105–112. 10.1016/j.jmaa.2003.09.072
Dahiya RS, Zafer A: Oscillation theorems of higher order neutral type differential equations. Dynamical systems and differential equations. Discrete and Continuous Dynamical Systems 1998, 203–219. Added Volume I Added Volume I
Das P: Oscillation criteria for odd order neutral equations. Journal of Mathematical Analysis and Applications 1994,188(1):245–257. 10.1006/jmaa.1994.1425
Erbe LH, Kong Q, Zhang BG: Oscillation Theory for Functional-Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics. Volume 190. Marcel Dekker, New York, NY, USA; 1995:viii+482.
Gopalsamy K, Lalli BS, Zhang BG: Oscillation of odd order neutral differential equations. Czechoslovak Mathematical Journal 1992,42(117)(2):313–323.
Grace SR, Lalli BS: Oscillation theorems for certain neutral differential equations. Czechoslovak Mathematical Journal 1988,38(113)(4):745–753.
Grace SR: Oscillation criteria forth order neutral functional-differential equations. Journal of Mathematical Analysis and Applications 1994,184(1):44–55. 10.1006/jmaa.1994.1182
Grace SR: On the oscillations of mixed neutral equations. Journal of Mathematical Analysis and Applications 1995,194(2):377–388. 10.1006/jmaa.1995.1306
Graef JR, Qian C, Yang B: Positive solutions of a higher order neutral differential equation. Mathematische Nachrichten 2003,256(1):17–28. 10.1002/mana.200310067
Kiguradze IT: On the oscillatory character of solutions of the equation. MatematicheskiÄ Sbornik 1964, 65 (107): 172–187.
Kitamura Y: Oscillation of functional-differential equations with general deviating arguments. Hiroshima Mathematical Journal 1985,15(3):445–491.
Ladas G, Sficas YG: Oscillations of neutral delay differential equations. Canadian Mathematical Bulletin 1986,29(4):438–445. 10.4153/CMB-1986-069-2
Ladas G, Sficas YG: Oscillations of higher-order neutral equations. Journal of the Australian Mathematical Society 1986,27(4):502–511. 10.1017/S0334270000005105
Philos ChG, Purnaras IK, Sficas YG: Oscillations in higher-order neutral differential equations. Canadian Journal of Mathematics 1993,45(1):132–158. 10.4153/CJM-1993-008-6
Ouyang Z, Tang Q: Oscillation criteria for a class of higher order neutral differential equations. Annals of Differential Equations 2003,19(1):65–70.
Saker SH: Oscillation of higher order neutral delay differential equations with variable coefficients. Dynamic Systems and Applications 2002,11(1):107–125.
Staïkos VA: Basic results on oscillation for differential equations with deviating arguments. Hiroshima Mathematical Journal 1980,10(3):495–516.
Tanaka S: Oscillation of solutions of even order neutral differential equations. Dynamic Systems and Applications 2000,9(3):353–360.
Wang P, Shi W: Oscillatory theorems of a class of even-order neutral equations. Applied Mathematics Letters 2003,16(7):1011–1018. 10.1016/S0893-9659(03)90088-7
Wang P, Wang M: Oscillation of a class of higher order neutral differential equations. Archivum Mathematicum 2004,40(2):201–208.
Wang P: Oscillations ofth-order neutral equation with continuous distributed deviating arguments. Annals of Differential Equations 1998,14(3):570–575.
Wang Z: A necessary and sufficient condition for the oscillation of higher-order neutral equations. The Tohoku Mathematical Journal 1989,41(4):575–588. 10.2748/tmj/1178227728
Yang B, Zhang BG: Oscillation of a class of higher order neutral differential equations. Mathematische Nachrichten 1998, 193: 243–253. 10.1002/mana.19981930116
Zhang G: Eventually positive solutions of odd order neutral differential equations. Applied Mathematics Letters 2000,13(6):55–61. 10.1016/S0893-9659(00)00054-9
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Dahiya, R., Zafer, A. Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments. J Inequal Appl 2007, 098423 (2007). https://doi.org/10.1155/2007/98423
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2007/98423