Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations
2001 ◽
Vol 27
(2)
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pp. 69-76
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Keyword(s):
The authors consider themth order nonlinear difference equations of the formDmyn+qnf(yσ(n))=ei, wherem≥1,n∈ℕ={0,1,2,…},ani>0fori=1,2,…,m−1,anm≡1,D0yn=yn,Diyn=aniΔDi−1yn,i=1,2,…,m,σ(n)→∞asn→∞, andf:ℝ→ℝis continuous withuf(u)>0foru≠0. They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero asn→∞without assuming that∑n=0∞1/ani=∞,i=1,2,…,m−1,{qn}is positive, oren≡0as is often required. If{qn}is positive, they prove another such result for all nonoscillatory solutions.
2018 ◽
Vol 71
(1)
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pp. 139-148
1996 ◽
Vol 39
(3)
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pp. 525-533
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2011 ◽
Vol 2011
◽
pp. 1-11
2015 ◽
Vol 2015
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pp. 1-10
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2007 ◽
Vol 333
(2)
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pp. 1203-1215
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2004 ◽
Vol 10
(11)
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pp. 1033-1036