Oscillation of fourth-order delay dynamic equations

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• 作者：ChengHui Zhang (1)
  Ravi P. Agarwal (2)
  Martin Bohner (3)
  TongXing Li (1) (4)
  
  1. School of Control Science and Engineering ; Shandong University ; Jinan ; 250061 ; China
  2. Department of Mathematics ; Texas A&M University-Kingsville ; 700 University Blvd. ; Kingsville ; TX ; 78363-8202 ; USA
  3. Department of Mathematics and Statistics ; Missouri University of Science and Technology ; Rolla ; MO ; 65409-0020 ; USA
  4. Department of Mathematics ; Linyi University ; Linyi ; 276005 ; China
  
• 关键词：Swift ; Hohenberg equation ; oscillation ; delay dynamic equation ; fourth ; order ; time scale ; 34K11 ; 34N05 ; 39A10
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：58
• 期：1
• 页码：143-160
• 全文大小：243 KB
• 参考文献：1. Agarwal R P, Akin-Bohner E, Sun S. Oscillation criteria for fourth-order nonlinear dynamic equations. Comm Appl Nonlinear Anal, 2011, 18: 1鈥?6
  2. Agarwal R P, Bohner M. An oscillation criterion for first order delay dynamic equations. Funct Differ Equ, 2009, 16: 11鈥?7
  3. Agarwal R P, Bohner M, Saker S H. Oscillation of second order delay dynamic equations. Can Appl Math Q, 2005, 13: 1鈥?7
  4. Agarwal R P, Grace S R, O鈥橰egan D. Oscillation criteria for certain / nth order differential equations with deviating arguments. J Math Anal Appl, 2001, 262: 601鈥?22 CrossRef
  5. Agarwal R P, Grace S R, O鈥橰egan D. Oscillation Theory for Second Order Dynamic Equations, volume 5 of Series in Mathematical Analysis and Applications. London: Taylor and Francis Ltd., 2003 CrossRef
  6. Akin-Bohner E, Bohner M, Saker S H. Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations. Electron Trans Numer Anal, 2007, 27: 1鈥?2
  7. Anderson D R, Saker S H. Interval oscillation criteria for forced Emden-Fowler functional dynamic equations with oscillatory potential. Sci China Math, 2013, 56: 561鈥?76 CrossRef
  8. Bartu拧ek M, Cecchi M, Do拧l谩 Z, et al. Fourth-order differential equation with deviating argument. Abstr Appl Anal, 2012, 2012: 1鈥?7
  9. Berchio E, Ferrero A, Gazzola F, et al. Qualitative behavior of global solutions to some nonlinear fourth order differential equations. J Differential Equations, 2011, 251: 2696鈥?727 CrossRef
  10. Bohner M, Peterson A. Dynamic Equations on Time Scales: An Introduction with Applications. Boston: Birkh盲user, 2001 CrossRef
  11. Bohner M, Peterson A. Advances in Dynamic Equations on Time Scales. Boston: Birkh盲user, 2003 CrossRef
  12. Erbe L. Oscillation criteria for second order linear equations on a time scale. Can Appl Math Q, 2001, 9: 345鈥?75
  13. Erbe L, Peterson A, Saker S H. Hille and Nehari type criteria for third-order dynamic equations. J Math Anal Appl, 2007, 329: 112鈥?31 CrossRef
  14. Erbe L, Peterson A, Saker S H. Oscillation criteria for second-order nonlinear delay dynamic equations. J Math Anal Appl, 2007, 333: 505鈥?22 CrossRef
  15. Fite W B. Concerning the zeros of the solutions of certain differential equations. Trans Amer Math Soc, 1918, 19: 341鈥?52 CrossRef
  16. Grace S R. Oscillation of even order nonlinear functional differential equations with deviating arguments. Math Slovaca, 1991, 41: 189鈥?04
  17. Grace S R, Agarwal R P, Bohner M, et al. Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations. Commun Nonlinear Sci Numer Simul, 2009, 14: 3463鈥?471 CrossRef
  18. Grace S R, Agarwal R P, Pinelas S. On the oscillation of fourth order superlinear dynamic equations on time scales. Dynam Systems Appl, 2011, 20: 45鈥?4
  19. Grace S R, Agarwal R P, Sae-jie W. Monotone and oscillatory behavior of certain fourth order nonlinear dynamic equations. Dynam Systems Appl, 2010, 19: 25鈥?2
  20. Grace S R, Bohner M, Sun S. Oscillation of fourth-order dynamic equations. Hacet J Math Stat, 2010, 39: 545鈥?53
  21. Grace S R, Lalli B S. Oscillation theorems for / n-th order delay differential equations. J Math Anal Appl, 1983, 91: 352鈥?66 CrossRef
  22. Grace S R, Lalli B S. Oscillation theorems for / nth order nonlinear differential equations with deviating arguments. Proc Amer Math Soc, 1984, 90: 65鈥?0
  23. Grace S R, Lalli B S. Oscillation theorems for damped differential equations of even order with deviating arguments. SIAM J Math Anal, 1984, 15: 308鈥?16 CrossRef
  24. Hassan T S. Oscillation of third order nonlinear delay dynamic equations on time scales. Math Comput Modelling, 2009, 49: 1573鈥?586 CrossRef
  25. Hilger S. Analysis on measure chains-a unified approach to continuous and discrete calculus. Results Math, 1990, 18: 18鈥?6 CrossRef
  26. Howard H C. Oscillation criteria for even order differential equations. Ann Mat Pura Appl, 1964, 66: 221鈥?31 CrossRef
  27. Karpuz B, 脰calan 脰, 脰zt眉rk S. Comparison theorems on the oscillation and asymptotic behavior of higher-order neutral differential equations. Glasg Math J, 2010, 52: 107鈥?14 CrossRef
  28. Kiguradze I T, Chanturia T A. Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations. Dordrecht: Kluwer Academic Publishers, 1993 CrossRef
  29. Li T, Han Z, Sun S, et al. Oscillation results for third order nonlinear delay dynamic equations on time scales. Bull Malays Math Sci Soc, 2011, 34: 639鈥?48
  30. Li T, Thandapani E, Tang S. Oscillation theorems for fourth-order delay dynamic equations on time scales. Bull Math Anal Appl, 2011, 3: 190鈥?99
  31. Peletier L A, Troy W C. Spatial Patterns: Higher Order Models in Physics and Mechanics. Boston, MA: Birkh盲user Boston Inc., 2001 CrossRef
  32. 艠eh谩k P. How the constants in Hille-Nehari theorems depend on time scales. Adv Difference Equ, 2006, 2006: 1鈥?5
  33. S艧ahiner Y. Oscillation of second-order delay differential equations on time scales. Nonlinear Anal, 2005, 63: 1073鈥?080 CrossRef
  34. Saker S H. Oscillation Theory of Dynamic Equations on Time Scales, Second and Third Orders. Berlin: Lambert Academic Publishing, 2010
  35. Thandapani E, Piramanantham V, Pinelas S. Oscillation theorems of fourth order nonlinear dynamic equations on time scales. Int J Pure Appl Math, 2012, 76: 455鈥?68
  36. Zafer A. Oscillation criteria for even order neutral differential equations. Appl Math Lett, 1998, 11: 21鈥?5 CrossRef
  37. Zhang C, Li T, Agarwal R P, et al. Oscillation results for fourth-order nonlinear dynamic equations. Appl Math Lett, 2012, 25: 2058鈥?065 CrossRef
  38. Zhang Q, Yan J. Oscillation behavior of even order neutral differential equations with variable coefficients. Appl Math Lett, 2006, 19: 1202鈥?206 CrossRef
  39. Zhang Q, Yan J, Gao L. Oscillation behavior of even-order nonlinear neutral differential equations with variable coefficients. Comput Math Appl, 2010, 59: 426鈥?30 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale. In the general time scales case, four oscillation theorems are presented that can be used in cases where known results fail to apply. The results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time scale. These criteria improve a number of related contributions to the subject. Some illustrative examples are provided.