caa a22 4500 388092165 CHVBK 20180307125254.0 cr unu---uuuuu 161130e199908 xx s 000 0 eng 10.1017/S0004972700033360 doi S0004972700033360 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700033360 Oscillation criteria for certain second order nonlinear difference equations [Elektronische Daten] 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. Copyright © Australian Mathematical Society 1999 Grace S.R. Department of Engineering Mathematics Faculty of Engineering Cairo University Orman Giza 1200 Egypt El-Morshedy H.A. Department of Mathematics and Statistics The Flinders University of South Australia GPO Box 2100 Adelaide SA 5001 Australia Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 95-108 0004-9727 60:1<95 1999 60 BAZ https://doi.org/10.1017/S0004972700033360 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700033360 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grace S.R. Department of Engineering Mathematics Faculty of Engineering Cairo University Orman Giza 1200 Egypt NATIONALLICENCE 700 1- El-Morshedy H.A. Department of Mathematics and Statistics The Flinders University of South Australia GPO Box 2100 Adelaide SA 5001 Australia NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 95-108 0004-9727 60:1<95 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge