Global Behavior of the Difference Equationxn+1=(p+xn-1)/(qxn+xn-1)
نویسندگان
چکیده
منابع مشابه
Global Behavior of the Difference Equation
The main objective of this paper is to study the qualitative behavior for a class of nonlinear rational difference equation. We study the local stability, periodicity, Oscillation, boundedness, and the global stability for the positive solutions of equation. Examples illustrate the importance of the results Keywords— Difference equation, stability, oscillation, boundedness, globale stability an...
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 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 solutions of some difference equations
where the initial conditions x-r, x-r+1, x-r+2,..., x0 are arbitrary positive real numbers, r = max{l, k, p, q} is nonnegative integer and a, b, c are positive constants: Moreover, we obtain the form of the solution of some special cases of Equation 1 and some numerical simulations to the equation are given to illustrate our results. Let us introduce some basic definitions and some theorems tha...
متن کاملGlobal Behavior of Two Families of Nonlinear Symmetric Difference Equations
We mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in Stević’s paper 2010 . A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of Aloqeili 2009 , Berenha...
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: Abstract and Applied Analysis
سال: 2010
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2010/237129