Displaying similar documents to “Asymptotic properties of solutions of higher order difference equations”

Asymptotic behavior of solutions of nonlinear difference equations

Janusz Migda (2004)

Mathematica Bohemica

Similarity:

The nonlinear difference equation x n + 1 - x n = a n ϕ n ( x σ ( n ) ) + b n , ( E ) where ( a n ) , ( b n ) are real sequences, ϕ n ℝ ⟶ ℝ , ( σ ( n ) ) is a sequence of integers and lim n ⟶ ∞ σ ( n ) = ∞ , is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation y n + 1 - y n = b n are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also 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

Similarity:

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.