Boundedness character of positive solutions of a higher order difference equation

نویسندگان

  • Kenneth S. Berenhaut
  • John D. Foley
  • Stevo Stevic
چکیده

Recently there has been a great deal of interest in studying the behaviour of rational difference equations. One of the properties which has attracted considerable attention from the experts in the research field is the boundedness character (see, e.g. [1–32] and the related references therein). This paper studies the boundedness character of positive solutions of the recursive equation yn = A+ yn−k yn−m , n ∈ N0, (1)

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

STUDYING THE BEHAVIOR OF SOLUTIONS OF A SECOND-ORDER RATIONAL DIFFERENCE EQUATION AND A RATIONAL SYSTEM

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.  

متن کامل

On the Dynamic of a Nonautonomous

Nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. The study of dynamical properties of such equations is of great importance in many areas. The autonomous difference equat...

متن کامل

Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

متن کامل

Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: yn 1 r pyn yn−k / qyn yn−k , n ∈ N0, where the parameters p, q, r ∈ 0,∞ , k ∈ {1, 2, 3, . . .} and the initial conditions y−k, . . . , y0 ∈ 0,∞ . We show that the unique positive equilibrium of this equation is ...

متن کامل

On a class of third-order nonlinear difference equations

This paper studies the boundedness character of the positive solutions of the difference equation x(n+1) = A + x(n)^p/(x(n-1)^q*x(n-2)^r), no, where the parameters A, p, q and r are positive numbers.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Int. J. Comput. Math.

دوره 87  شماره 

صفحات  -

تاریخ انتشار 2010