Abstract
We consider the difference equation with continuous argument
where λ > 0, t ∈ [0, ∞), and f: [0, ∞) × R → R. Conditions for the existence and uniqueness of continuous asymptotically periodic solutions of this equation are given. We also prove the following result: Let x(t) be a real continuous function such that
for some α ∈ R. Then it always follows from the boundedness of x(t) that
t → ∞ if and only if α ∈ R {1}.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1095–1100, August, 2004.
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Stević, S. Asymptotic behavior of solutions of a nonlinear difference equation with continuous argument. Ukr Math J 56, 1300–1307 (2004). https://doi.org/10.1007/s11253-005-0058-1
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DOI: https://doi.org/10.1007/s11253-005-0058-1