Displaying similar documents to “Asymptotic properties for half-linear 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.

Asymptotic behavior of solutions of nonlinear difference equations

Janusz Migda (2004)

Mathematica Bohemica

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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.