The matrix equation Xn = A
نویسندگان
چکیده
منابع مشابه
On the Max-Type Difference Equation xn+1=max{A/xn,xn-3}
The study of max-type difference equations attracted recently a considerable attention, see, for example, 1–27 , and the references listed therein. This type of difference equations stems from, for example, certain models in automatic control theory see 28 . In the beginning of the study of these equations experts have been focused on the investigation of the behavior of some particular cases o...
متن کاملON BOUNDEDNESS OF THE SOLUTIONS OF THE DIFFERENCE EQUATION xn+1=xn-1/(p+xn)
Theorem 1. (i) If p > 1, then the unique equilibrium 0 of (1) is globally asymptotically stable. (ii) If p = 1, then every positive solution of (1) converges to a period-two solution. (iii) If 0 < p < 1, then 0 and x = 1− p are the only equilibrium points of (1), and every positive solution {xn}n=−1 of (1) with (xN − x)(xN+1 − x) < 0 for some N ≥ −1 is unbounded. They proposed the following ope...
متن کاملThe Periodic Character of the Difference Equation xn+1=f(xn-l+1,xn-2k+1)
In this paper, we consider the nonlinear difference equation xn 1 f xn−l 1, xn−2k 1 , n 0, 1, . . . , where k, l ∈ {1, 2, . . . } with 2k / l and gcd 2k, l 1 and the initial values x−α, x−α 1, . . . , x0 ∈ 0, ∞ with α max{l − 1, 2k − 1}. We give sufficient conditions under which every positive solution of this equation converges to a not necessarily prime 2-periodic solution, which extends and ...
متن کاملGlobal Behavior of the Max-Type Difference Equation xn+1=max{1/xn,An/xn-1}
and Applied Analysis 3 Lemma 2.5. Let {xn}n −1 be a positive solution of 1.1 and limn→∞Pn S. Then S lim supn→∞xn. Proof. Since Pn is a subsequence of xn, it follows that S ≤ lim sup n→∞ xn. 2.6 On the other hand, by xn 1 ≤ Pn for all n ≥ 1, we obtain lim sup n→∞ xn ≤ lim sup n→∞ Pn S. 2.7 The proof is complete. Remark 2.6. Let {xn}n −1 be a positive solution of 1.1 . By Lemma 2.2, we see that i...
متن کاملGlobal Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)
and Applied Analysis 3 In the sequel, let q > 1 4p and . . . , φ, ψ, φ, ψ, . . . the unique prime period-two solution of 1.1 with φ < ψ. Define f ∈ C φ, ψ × φ, ψ , φ, ψ by f ( x, y ) p y qx y 2.2 for any x, y ∈ φ, ψ and g ∈ C φ, ψ , φ, ψ by y∗ g ( y ) p y − y2 qy 2.3 for any y ∈ φ, ψ . Then
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1980
ISSN: 0021-8693
DOI: 10.1016/0021-8693(80)90309-9