E. M. Elsayed

Solutions of rational difference systems of order two

In this paper, we deal with the form of the solutions of the following rational difference system xn+1=xn−1±1+xn−1yn,yn+1=yn−1∓1+yn−1xn, with nonzero real number initial conditions.

ON THE DIFFERENCE EQUATION xn+1 = axn − bxn/(cxn − dxn−1)

We investigate some qualitative behavior of the solutions of the difference equation xn+ = axn - bxn/(cxx - dxn-1), n = 0,1,..., where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants.

Solution and Attractivity for a Rational Recursive Sequence

This paper is concerned with the behavior of solution of the nonlinear difference equation 𝑥𝑛

On the solutions of systems of rational difference equations

Abstract In this paper we deal with the periodic nature and the form of the solutions of the following systems of rational difference equations x n + 1 = x n − 3 ± 1 ± x n − 3 y n − 1 , y n + 1 = y n − 3 ± 1 ± y n − 3 x n − 1 with a nonzero real number’s initial conditions.

Global behavior of the solutions of some difference equations

AbstractIn this article we study the difference equation xn+1=axn-lxn-kbxn-p-cxn-q,n=0,1,…, 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: Also, we study some special cases of this equation.

On the Difference equation xn+ = axn - bxn/(cxx - dxn-1)

We investigate some qualitative behavior of the solutions of the difference equation xn+ = axn - bxn/(cxx - dxn-1), n = 0,1,..., where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants.

ON THE PERIODIC NATURE OF SOME MAX-TYPE DIFFERENCE EQUATIONS

We study some qualitative behavior of solutions of some max-type difference equations with periodic coefficients. Some new results of the periodicity character of solutions of that type of difference equations will be established.

On the solutions of some nonlinear systems of difference equations

AbstractIn this paper, we deal with the existence of solutions and the periodicity character of the following systems of rational difference equations with order three: xn+1=xnyn−2yn−1(±1±xnyn−2),yn+1=ynxn−2xn−1(±1±ynxn−2), where the initial conditions x−2, x−1, x0, y−2, y−1 and y0 are nonzero real numbers.MSC:39A10.

On the Solutions of a General System of Difference Equations

We deal with the solutions of the systems of the difference equations , , and , , , with a nonzero real numbers initial conditions. Also, the periodicity of the general system of variables will be considered.

Dynamics of Recursive Sequence of Order Two

In this paper we study some qualitative behavior of the solutions of the difference equation xn+1 = axn + bxn cxn − dxn 1 ; n = 0; 1;:::; where the initial conditions x 1; x0 are arbitrary real numbers and a;b;c;d are positive constants with cx0 − dx 1 0.