Displaying similar documents to “Oscillatory solutions for second-order difference equations in Hilbert spaces.”

On oscillation and nonoscillation properties of Emden-Fowler difference equations

Mariella Cecchi, Zuzana Došlá, Mauro Marini (2009)

Open Mathematics

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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.

Global attractivity of the equilibrium of a nonlinear difference equation

John R. Graef, C. Qian (2002)

Czechoslovak Mathematical Journal

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The authors consider the nonlinear difference equation x n + 1 = α x n + x n - k f ( x n - k ) , n = 0 , 1 , ⋯ . 1 where α ∈ ( 0 , 1 ) , k ∈ { 0 , 1 , ⋯ } and f ∈ C 1 [ [ 0 , ∞ ) , [ 0 , ∞ ) ] ( 0 ) with f ' ( x ) < 0 . They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.