Necessary Conditions for the Solutions of Second Order Non-linear Neutral Delay Difference Equations to Be Oscillatory or Tend to Zero
2007 ◽
Vol 2007
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pp. 1-16
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Keyword(s):
We find necessary conditions for every solution of the neutral delay difference equationΔ(rnΔ(yn−pnyn−m))+qnG(yn−k)=fnto oscillate or to tend to zero asn→∞, whereΔis the forward difference operatorΔxn=xn+1−xn, andpn, qn, rnare sequences of real numbers withqn≥0, rn>0. Different ranges of{pn}, includingpn=±1, are considered in this paper. We do not assume thatGis Lipschitzian nor nondecreasing withxG(x)>0forx≠0. In this way, the results of this paper improve, generalize, and extend recent results. Also, we provide illustrative examples for our results.
2007 ◽
Vol 38
(4)
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pp. 323-333
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2018 ◽
Vol 2018
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pp. 1-13
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2018 ◽
Vol 2018
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pp. 1-8
2001 ◽
Vol 28
(5)
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pp. 301-306
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1994 ◽
Vol 17
(3)
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pp. 619-623
2018 ◽
Vol 72
(1)
◽
pp. 19