Displaying similar documents to “Asymptotic behavior of solutions of nonlinear difference equations”

Asymptotic properties of solutions of higher order difference equations

Janusz Migda (2010)

Mathematica Bohemica

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Asymptotic properties of solutions of the difference equation of the form Δ m x n = a n ϕ ( x τ 1 ( n ) , ⋯ , x τ k ( n ) ) + b n are studied. Conditions under which every (every bounded) solution of the equation Δ m y n = b n is asymptotically equivalent to some solution of the above equation are obtained.

On the rational recursive sequence x n + 1 = A + ∑ i = 0 k α i x n - i / ∑ i = 0 k β i x n - i

E. M. E. Zayed, M. A. El-Moneam (2008)

Mathematica Bohemica

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The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation x n + 1 = A + ∑ i = 0 k α i x n - i / ∑ i = 0 k β i x n - i , n = 0 , 1 , 2 , ⋯ where the coefficients A , α i , β i and the initial conditions x - k , x - k + 1 , ⋯ , x - 1 , x 0 are positive real numbers, while k is a positive integer number.