Oscillation of third-order delay difference equations with negative damping term

Martin Bohner, Srinivasan Geetha, Srinivasan Selvarangam, Ethiraju Thandapani

Abstract


The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results.


Keywords


Third-order delay difference equation; comparison theorems; oscillation; asymptotic behavior

Full Text:

PDF

References


Agarwal, R. P., Difference Equations and Inequalities. Theory, Methods, and Applications, Marcel Dekker, Inc., New York, 2000.

Agarwal, R. P., Bohner, M., Grace, S. R., O’Regan, D., Discrete Oscillation Theory, Hindawi Publishing Corporation, New York, 2005.

Agarwal R. P., Grace, S. R., Oscillation of certain third-order difference equations, Comput. Math. Appl. 42 (3-5) (2001), 379-384,

Agarwal, R. P., Grace, S. R., O’Regan, D., On the oscillation of certain third-order difference equations, Adv. Difference Equ. 3 (2005), 345-367.

Aktas, M. F., Tiryaki, A., Zafer, A., Oscillation of third-order nonlinear delay difference equations, Turkish J. Math. 36 (3) (2012), 422-436.

Bohner, M., Dharuman, C., Srinivasan, R., Thandapani, E., Oscillation criteria for third-order nonlinear functional difference equations with damping, Appl. Math. Inf. Sci. 11 (3) (2017), 669-676.

Grace, S. R., Agarwal, R. P., Graef J. R., Oscillation criteria for certain third order nonlinear difference equations, Appl. Anal. Discrete Math. 3 (1) (2009), 27-38.

Graef, J. R., Thandapani, E., Oscillatory and asymptotic behavior of solutions of third order delay difference equations, Funkcial. Ekvac. 42 (3) (1999), 355-369.

Gyori, I., Ladas, G., Oscillation Theory of Delay Differential Equations. With Applications, The Clarendon Press, Oxford University Press, New York, 1991,

Parhi, N., Panda, A., Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order, Math. Bohem. 133 (1) (2008), 99-112.

Saker, S. H., Alzabut, J. O., Mukheimer, A., On the oscillatory behavior for a certain class of third order nonlinear delay difference equations, Electron. J. Qual. Theory Differ. Equ. 67 (2010), 16 pp.

Smith, B., Oscillation and nonoscillation theorems for third order quasi-adjoint difference equations, Portugal. Math. 45 (3) (1988), 229-243.

Smith, B., Taylor, Jr., W. E., Nonlinear third-order difference equations: oscillatory and asymptotic behavior, Tamkang J. Math. 19 (3) (1988), 91-95.

Tang, X., Liu, Y., Oscillation for nonlinear delay difference equations, Tamkang J. Math. 32 (4) (2001), 275-280.

Thandapani, E., Mahalingam, K., Oscillatory properties of third order neutral delay difference equations, Demonstratio Math. 35 (2) (2002), 325-337.

Thandapani, E., Pandian, S., Balasubramaniam, R. K., Oscillatory behavior of solutions of third order quasilinear delay difference equations, Stud. Univ. Zilina Math. Ser. 19 (1) (2005), 65-78.

Thandapani, E., Selvarangam, S., Oscillation theorems for second order quasilinear neutral difference equations, J. Math. Comput. Sci. 2 (4) (2012), 866-879.




DOI: http://dx.doi.org/10.17951/a.2018.72.1.19-28
Date of publication: 2018-06-25 09:04:03
Date of submission: 2018-06-24 16:43:54


Statistics


Total abstract view - 1451
Downloads (from 2020-06-17) - PDF - 729

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Martin Bohner, Srinivasan Geetha, Srinivasan Selvarangam, Ethiraju Thandapani