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- W2023668359 abstract "We consider the difference equation $$ {Delta^2}u(k) + sumlimits_{l = 1}^m {{p_l}(k)uleft( {{tau_l}(k)} right) = 0}, $$ where m ∈ N, the functions p l : N → R + and τ l : N → N, lim k→+∞ τ l (k) = +∞, l = 1, …, m, are defined on the set of natural numbers, and the difference operator is defined as follows: Δu(k) = u(k + 1) − u(k), Δ2 = Δ ◦ Δ. We establish necessary conditions for the above equation to have a positive solution. We also obtain oscillation criteria of a new type that generalize some earlier known results." @default.
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- W2023668359 date "2009-04-01" @default.
- W2023668359 modified "2023-09-27" @default.
- W2023668359 title "Necessary conditions for the existence of positive solutions of second-order linear difference equations and sufficient conditions for the oscillation of solutions" @default.
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- W2023668359 doi "https://doi.org/10.1007/s11072-009-0071-7" @default.
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