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Oscillation criteria for certain second order nonlinear difference equations

Published online by Cambridge University Press:  17 April 2009

S.R. Grace  and
H.A. El-Morshedy
S.R. Grace
Affiliation:
Department of Engineering MathematicsFaculty of EngineeringCairo UniversityOrmanGiza 1200Egypt
H.A. El-Morshedy
Affiliation:
Department of Mathematics and StatisticsThe Flinders University of South AustraliaGPO Box 2100Adelaide SA 5001Australia
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Abstract

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This paper is concerned with nonlinear difference equations of the form

where δ is the forward difference operator defined by δun−1 = un − un −1 δ2un −1= δ(δun-1) and {an} is a real sequence which is not assumed to be nonnegative. The function f is such that uf(u) < 0 for all u ≠ 0 and f(u) − f(v) = g(u, v)(u − v), for all u, v ≠ 0, and for some nonnegative function g. Our results are not only new but also improve and generalise some recent oscillation criteria. Examples illustrating the importance of our main results are also given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 95 - 108
Copyright
Copyright © Australian Mathematical Society 1999

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