Open Access

Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments

Journal of Inequalities and Applications20072007:098423

https://doi.org/10.1155/2007/98423

Received: 19 October 2006

Accepted: 15 May 2007

Published: 2 September 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.

[12345678910111213141516171819202122232425262728]

Authors’ Affiliations

(1)
Department of Mathematics, Iowa State University
(2)
Department of Mathematics, Middle East Technical University

References

  1. Hale J: Theory of Functional Differential Equations. 2nd edition. Springer, New York, NY, USA; 1977:x+365.View ArticleMATHGoogle Scholar
  2. Agarwal RP, Grace SR, O'Regan D: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic Publishers, Dordrecht, The Netherlands; 2000:viii+337.View ArticleMATHGoogle Scholar
  3. 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)00280-1MathSciNetView ArticleMATHGoogle Scholar
  4. Baĭnov DD, Mishev DP: Oscillation Theory for Neutral Differential Equations with Delay. IOP, Bristol, UK; 1992.Google Scholar
  5. 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.2003.09.072MathSciNetView ArticleMATHGoogle Scholar
  6. 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 IGoogle Scholar
  7. Das P: Oscillation criteria for odd order neutral equations. Journal of Mathematical Analysis and Applications 1994,188(1):245–257. 10.1006/jmaa.1994.1425MathSciNetView ArticleMATHGoogle Scholar
  8. 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.Google Scholar
  9. Gopalsamy K, Lalli BS, Zhang BG: Oscillation of odd order neutral differential equations. Czechoslovak Mathematical Journal 1992,42(117)(2):313–323.MathSciNetGoogle Scholar
  10. Grace SR, Lalli BS: Oscillation theorems for certain neutral differential equations. Czechoslovak Mathematical Journal 1988,38(113)(4):745–753.MathSciNetGoogle Scholar
  11. Grace SR: Oscillation criteria forth order neutral functional-differential equations. Journal of Mathematical Analysis and Applications 1994,184(1):44–55. 10.1006/jmaa.1994.1182MathSciNetView ArticleMATHGoogle Scholar
  12. Grace SR: On the oscillations of mixed neutral equations. Journal of Mathematical Analysis and Applications 1995,194(2):377–388. 10.1006/jmaa.1995.1306MathSciNetView ArticleMATHGoogle Scholar
  13. 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.200310067MathSciNetView ArticleMATHGoogle Scholar
  14. Kiguradze IT: On the oscillatory character of solutions of the equation. Matematicheskiĭ Sbornik 1964, 65 (107): 172–187.MathSciNetGoogle Scholar
  15. Kitamura Y: Oscillation of functional-differential equations with general deviating arguments. Hiroshima Mathematical Journal 1985,15(3):445–491.MathSciNetMATHGoogle Scholar
  16. Ladas G, Sficas YG: Oscillations of neutral delay differential equations. Canadian Mathematical Bulletin 1986,29(4):438–445. 10.4153/CMB-1986-069-2MathSciNetView ArticleMATHGoogle Scholar
  17. Ladas G, Sficas YG: Oscillations of higher-order neutral equations. Journal of the Australian Mathematical Society 1986,27(4):502–511. 10.1017/S0334270000005105MathSciNetView ArticleMATHGoogle Scholar
  18. 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-1993-008-6MathSciNetView ArticleMATHGoogle Scholar
  19. Ouyang Z, Tang Q: Oscillation criteria for a class of higher order neutral differential equations. Annals of Differential Equations 2003,19(1):65–70.MathSciNetMATHGoogle Scholar
  20. Saker SH: Oscillation of higher order neutral delay differential equations with variable coefficients. Dynamic Systems and Applications 2002,11(1):107–125.MathSciNetMATHGoogle Scholar
  21. Staïkos VA: Basic results on oscillation for differential equations with deviating arguments. Hiroshima Mathematical Journal 1980,10(3):495–516.MathSciNetMATHGoogle Scholar
  22. Tanaka S: Oscillation of solutions of even order neutral differential equations. Dynamic Systems and Applications 2000,9(3):353–360.MathSciNetMATHGoogle Scholar
  23. 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)90088-7MathSciNetView ArticleMATHGoogle Scholar
  24. Wang P, Wang M: Oscillation of a class of higher order neutral differential equations. Archivum Mathematicum 2004,40(2):201–208.MathSciNetMATHGoogle Scholar
  25. Wang P: Oscillations ofth-order neutral equation with continuous distributed deviating arguments. Annals of Differential Equations 1998,14(3):570–575.MathSciNetMATHGoogle Scholar
  26. 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/1178227728MathSciNetView ArticleMATHGoogle Scholar
  27. Yang B, Zhang BG: Oscillation of a class of higher order neutral differential equations. Mathematische Nachrichten 1998, 193: 243–253. 10.1002/mana.19981930116MathSciNetView ArticleMATHGoogle Scholar
  28. Zhang G: Eventually positive solutions of odd order neutral differential equations. Applied Mathematics Letters 2000,13(6):55–61. 10.1016/S0893-9659(00)00054-9MathSciNetView ArticleMATHGoogle Scholar

Copyright

© R. S. Dahiya and A. Zafer 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.