Mathematica Bohemica, Vol. 144, No. 1, pp. 25-37, 2019


Oscillation theorems for third order nonlinear delay difference equations

Kumar S. Vidhyaa, Chinnappa Dharuman, Ethiraju Thandapani, Sandra Pinelas

Received February 19, 2017.   First published April 4, 2018.

Abstract:  Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form $\Delta(a_n(\Delta(b_n(\Delta y_n)^{\alpha})))+q_nf(y_{\sigma(n)})=0$ to have property ${(\rm A)}$ or to be oscillatory. These conditions improve and complement many known results reported in the literature. Examples are provided to illustrate the importance of the main results.
Keywords:  third order delay difference equation; property ${(\rm A)}$; comparison theorem
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Note: The same paper was published in International Journal of Pure and Applied Mathematics 114 (2017), No. 5, 151-164.
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Classification MSC:  39A10


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Affiliations:   Kumar S. Vidhyaa, Chinnappa Dharuman, Department of Mathematics, SRM University, Ramapuram Campus, Chennai-600 089, India, e-mail: vidyacertain@gmail.com, cdharuman55@gmail.com; Ethiraju Thandapani, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai-600 005, India, e-mail: ethandapani@yahoo.co.in; Sandra Pinelas, RUDN University, 6 Miklukho-Maklaya str., Moscow-117198, e-mail: sandra.pinelas@gmail.com


 
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