IJPAM: Volume 120, No. 3 (2018)

Title

OSCILLATION CRITERIA FOR SECOND ORDER
DIFFERENCE EQUATIONS WITH SEVERAL
NONLINEAR NEUTRAL TERMS

Authors

S. Mehar Banu$^1$, S. Nalini$^2$
$^1$Department of Mathematics
Government Arts College (Autonomous)
Salem, 636 007, Tamilnadu, INDIA
$^2$Research and Development Center
Bharathiar University
Coimbatore, 641046, Tamilnadu, INDIA

Abstract

In this paper we establish some new sufficient conditions for the oscillation of all solutions of second order difference equations with several nonlinear neutral terms of the form

\begin{displaymath}\Delta \left(a(n)\Delta \left(x(n)+\sum _{i=1}^{m} p_{i} (n)x... ...ha _{i} } (n-k_{i} )\right)\right)+q(n)x^{\beta }(n+1-\ell)= 0.\end{displaymath}

Using an elementary inequality we reduce the nonlinear neutral terms to linear neutral terms, four new oscillation criteria are obtained. Examples are included to illustrate the main results.

History

Received: February 27, 2018
Revised: May 2, 2018
Published: December 28, 2018

AMS Classification, Key Words

AMS Subject Classification: 39A11
Key Words and Phrases: second order, difference equation, oscillation, nonlinear neutral terms

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How to Cite?

DOI: 10.12732/ijpam.v120i3.12 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 3
Pages: 433 -


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