Publication Cover
Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 1
151
Views
34
CrossRef citations to date
0
Altmetric
Original Articles

Oscillation results for second-order nonlinear neutral delay dynamic equations on time scales

, &
Pages 1-17 | Received 27 Sep 2006, Published online: 10 Apr 2007

References

  • Agarwal , RP , Bohner , M and Saker , SH . 2006 . Oscillation of second order delay dynamic equations . The Canadian Applied Mathematics Quarterly , (In press)
  • Agarwal , RP , O’Regan , D and Saker , SH . 2004 . Oscillation criteria for second-order nonlinear neutral delay dynamic equations . Journal of Mathematical Analysis and Applications , 300 : 203 – 217 .
  • Agarwal , RP , O’Regan , DD and Saker , SH . 2006 . Oscillation criteria for nonlinear perturbed dynamic equations of second-order on time scales . Journal of Applied Mathematics and Computing , 20 ( 1–2 ) : 133 – 147 .
  • Akin Bohner , E and Hoffacker , J . 2003 . Oscillation properties of an Emden–Fowler type equations on discrete time scales . Journal of Difference Equations and Applications , 9 : 603 – 612 .
  • Akin Bohner , E , Bohner , M and Saker , SH . Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations . Electronic Transactions on Numerical Analysis , (In press)
  • Bohner , M and Peterson , A . 2001 . Dynamic Equations on Time Scales: An Introduction with Applications , Boston : Birkhäuser .
  • Bohner , M and Peterson , A . 2003 . Advances in Dynamic Equations on Time Scales , Boston : Birkhäuser .
  • Bohner , M and Saker , SH . 2004 . Oscillation of second order nonlinear dynamic equations on time scales . The Rocky Mountain Journal of Mathematics , 34 : 1239 – 1254 .
  • Erbe , L . 2001 . Oscillation criteria for second order linear equations on a time scale . The Canadian Applied Mathematics Quarterly. , 9 : 1 – 31 .
  • Erbe , L and Peterson , A . 2001 . Riccati equations on a measure chain . Proceedings of Conference on Dynamic Systems and Applications . 2001 , Atlanta. Edited by: Ladde , GS , Medhin , NG and Sambandham , M . Vol. 3 , pp. 193 – 199 . Dynamic Publishers .
  • Erbe , L and Peterson , A . 2002 . “ Oscillation criteria for second order matrix dynamic equations on a time scale, Special Issue on dynamic equations on time scales ” . In Journal of Computational and Applied Mathematics Edited by: Agarwal , RP , Bohner , M and O'Regan , D . Vol. 141 , 169 – 185 .
  • Erbe , L and Peterson , A . 2004 . Boundedness and oscillation for nonlinear dynamic equations on a time scale . Proceedings of the American Mathematical Society , 132 : 735 – 744 .
  • Erbe , L , Peterson , A and Saker , SH . 2003 . Oscillation criteria for second-order nonlinear dynamic equations on time scales . Journal of the London Mathematical Society , 67 : 701 – 714 .
  • Erbe , L , Peterson , A and Saker , SH . 2005 . Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales . Journal of Computational and Applied Mathematics , 181 ( 1 ) : 92 – 102 .
  • Erbe , L , Peterson , A and Saker , SH . 2006 . Kamenev-type oscillation criteria for second-order linear delay dynamic equations . Dynamic Systems and Applications , 15 : 65 – 78 .
  • Hilger , S . 1990 . Analysis on measure chains — a unified approach to continuous and discrete calculus . Results in Mathematics. , 18 : 18 – 56 .
  • Hille , E . 1948 . Non-oscillation theorems . Transactions of the American Mathematical Society , 64 : 234 – 252 .
  • Kamenev , IV . 1971 . Certain specifically nonlinear oscillation theorems . Mathematicheskie Zametki , 10 : 129 – 134 . (In Russian)
  • Kong , Q . 1999 . Interval criteria for oscillation of second-order linear ordinary differential equations . Journal of Mathematical Analysis and Applications , 229 : 258 – 270 .
  • Leighton , W . 1950 . The detection of the oscillation of solutions of a second order linear differential equation . Duke Mathematical Journal , 17 : 57 – 62 .
  • Philos , ChG . 1989 . Oscillation theorems for linear differential equation of second order . Archive for Mathematical Logic , 53 : 483 – 492 .
  • Saker , SH . 2004 . Oscillation of nonlinear dynamic equations on time scales . Applied Mathematics and Computation , 148 : 81 – 91 .
  • Saker , SH . 2005 . Oscillation criteria of second-order half-linear dynamic equations on time scales . Journal of Computational and Applied Mathematics , 177 : 375 – 387 .
  • Saker , SH . Boundedness of solutions of second-order forced nonlinear dynamic equations . The Rocky Mountain Journal of Mathematics , (To appear)
  • Saker , SH . 2005 . Oscillation of second-order forced nonlinear dynamic equations on time scales . Electronic Journal of Qualitative Theory of Differential Equations , 23 : 1 – 17 .
  • Saker , SH . 2006 . Oscillation of second-order nonlinear neutral delay dynamic equations on time scales . Journal of Computational and Applied Mathematics , 187 : 123 – 141 .
  • Saker , SH . New oscillation criteria for second-order nonlinear dynamic equations on time scales . Nonlinear Functional Analysis and Applications , (Accepted)
  • Zhang , G and Cheng , SS . 1999 . A necessary and sufficient oscillation condition for the discrete Euler equation . PanAmerican Mathematical Journal , 9 : 29 – 34 .
  • Wu , H-Wu , Zhuang , RK and Mathsen , RM . Oscillation criteria for second-order nonlinear neutral variable delay dynamic equations . Applied Mathematis and Computation , (In press)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.