IJPAM: Volume 103, No. 2 (2015)

OSCILLATION OF FIRST ORDER NON-LINEAR NEUTRAL
DIFFERENCE EQUATIONS OF RETARDED AND
ADVANCED TYPE

A. Murugesan$^1$, P. Selvakumar$^2$
$^1$Department of Mathematics
Government Arts College (Autonomous)
Salem, 636 007, Tamil Nadu, INDIA
$^2$Department of Mathematics
Dr. S.J.S. Paul Memorial College of
Engineering and Technology
Ramanathapuram Revenue Village
Villianur Commune, Puducherry, 605 502, Tamil Nadu, INDIA


Abstract. In this paper, we establish sufficient conditions for the oscillations for the all solutions of the first order non-linear neutral difference equations of retarded and advanced type. Our approach is to reduce the oscillation of neutral difference equations to the nonexistence of eventually positive solutions of non-neutral difference inequalities. Our results extend and improve several known results in the literature.

Received: April 13, 2015

AMS Subject Classification: 39A10, 39A12

Key Words and Phrases: first order difference equation, neutral, retarded, advanced, oscillation and nonoscillation properties

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DOI: 10.12732/ijpam.v103i2.10 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: 2015
Volume: 103
Issue: 2
Pages: 243 - 253


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