On third-order linear difference equations involving quasi-differences.

Došlá, Zuzana; Kobza, Aleš

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On oscillation and nonoscillation properties of Emden-Fowler difference equations

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A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation $Δ (a_{n} {|Δ x_{n}|}^{α} s g n Δ x_{n}) + b_{n} {|x_{n + 1}|}^{β} s g n x_{n + 1} = 0$ is given, jointly with some asymptotic properties. The problem of the coexistence of all possible types of nonoscillatory solutions is also considered and a comparison with recent analogous results, stated in the half-linear case, is made.