Asymptotic Solutions of nonlinear difference equations
نویسندگان
چکیده
منابع مشابه
Asymptotic Behavior of Solutions of Nonlinear Difference Equations
The nonlinear difference equation (E) xn+1 − xn = anφn(xσ(n)) + bn, where (an), (bn) are real sequences, φn : −→ , (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 yn+1 − yn = bn are given. Sufficient conditions under which for every real consta...
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The authors consider themth order nonlinear difference equations of the form Dmyn+qnf(yσ(n)) = ei, where m ≥ 1, n ∈N = {0,1,2, . . .}, an > 0 for i= 1,2, . . . ,m−1, an ≡ 1, D0yn = yn, Diyn = an∆Di−1yn, i = 1,2, . . . ,m, σ(n) → ∞ as n → ∞, and f : R → R is continuous with uf(u) > 0 for u = 0. They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero as n→...
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For ten nonlinear difference equations with only p-periodic solutions it is shown that the characteristic polynomials of the corresponding linearized equations about the equilibria have only zeros which are p-th roots of unity. An analogous result is shown concerning two systems of such equations. Five counterexamples show that the reverse is not true. Some remarks are made concerning equations...
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2008
ISSN: 0240-2963
DOI: 10.5802/afst.1196