Back
 JAMP  Vol.3 No.11 , November 2015
Boundedness and Oscillation of Third Order Neutral Differential Equations with Deviating Arguments
Abstract: we consider the third-order neutral functional differential equations with deviating arguments. A new theorem is presented that improves a number of results reported in the literature. Examples are included to illustrate new results.
Cite this paper: Elabbasy, E. , Barsoum, M. and Moaaz, O. (2015) Boundedness and Oscillation of Third Order Neutral Differential Equations with Deviating Arguments. Journal of Applied Mathematics and Physics, 3, 1367-1375. doi: 10.4236/jamp.2015.311164.
References

[1]   Agarwal, R.P., Aktas, M.F. and Tiryaki, A. (2009) On Oscillation Criteria for Third Order Nonlinear Delay Differential Equations. Archivum Mathematicum (Brno), 45, 1-18.

[2]   Aktas, M.F., Tiryaki, A. and Zafer, A. (2010) Oscillation Criteria for Third-Order Nonlinear Functional Differential Equations. Applied Mathematics Letters, 23, 756-762.
http://dx.doi.org/10.1016/j.aml.2010.03.003

[3]   Candan, T. and Dahiya, R.S. (2005) Functional Differential Equations of Third Order. Electronic Journal of Differential Equations, Conference 12, 47-56.

[4]   Dzurina, J. and Kotorova, R. (2008) Asymptotic Properties of Trinomial Delay Differential Equations. Archivum Mathematicum (Brno), 44, 149-158.

[5]   Dzurina, J. and Kotorova, R. (2009) Properties of the Third Order Trinomial Differential Equations with Argument. Nonlinear Analysis, 71, 1995-2002.
http://dx.doi.org/10.1016/j.na.2009.01.070

[6]   Elabbasy, E.M., Hassan, T.S. and Moaaz, O. (2012) Oscillation Behavior of Second Order Nonlinear Neutral Differential Equations with Deviating Arguments. Opuscula Mathematica, 32, 719-730.

[7]   El-sheikh, M.M., Sallam, R. and Mohamady, N. (2013) On the Oscillation of Third Order Neutral Delay Differential Equations. Applied Mathematics & Information Sciences Letters, 1, 77-80.

[8]   Erbe, L.H., Kong, Q. and Zhang, B.G. (1994) Oscillation Theory for Functional Differential Equations. Marcel Dekker, Inc., New York.

[9]   Graef, J.R., Savithri, R. and Thandapani, E. (2002) Oscillatory Properties of Third Order Neutral Delay Differential Equations. Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, 24-27 May 2002, 342-350.

[10]   Hale, J. (1977) Theory of Functional Differential Equations. 2nd Edition, Applied Mathematical Sciences Vol. 3, Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-9892-2

[11]   Su, M. and Xu, Z. (2012) Oscillation Criteria Of Certain Third Order Neutral Differential Equations. Differential Equations & Applications, 4, 221-232.
http://dx.doi.org/10.7153/dea-04-13

[12]   Li, T., Thandapani, E. and Graef, J.R. (2012) Oscillation of Third-Order Neutral Retarded Differential Equations. International Journal of Pure and Applied Mathematics, 75, 511-520.

[13]   Mihalikova, B. and Kostikova, E. (2009) Boundedness and Oscillation of Third Order Neutral Differential Equations, Tatra Mountains Mathematical Publications, 43, 137-144.
http://dx.doi.org/10.2478/v10127-009-0033-6

[14]   Jaros, J. and Kusano, T. (1990) On a Class of First Order Nonlinear Functional Differential Equations of Neutral Type. Czechoslovak Mathematical Journal, 40, 475-490.

 
 
Top