Elmetwally M. Elabbasy

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.

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.

Interval oscillation for second order sublinear differential equations with a damping term

We present new oscillation criteria for the second order nonlinear differential equation with a damping term (a(t)y′(t))′ + p(t)y′(t) + q(t)|y(t)|α−1y(t) = 0, t ≥ t0 where 0 < α ≤ 1. Our results here are different, generalise and improve some known results for oscillation of second order nonlinear differential equations that are different from most known ones in the sencse they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line and can be applied to extreme cases such as ∫t0∞ q(t)dt = −∞. Our results are illustrated with examples.

DYNAMICS OF A CLASS OF NON-AUTONOMOUS SYSTEMS OF TWO NON-INTERACTING PREYS WITH COMMON PREDATOR

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

OSCILLATION AND STABILITY OF NONLINEAR DISCRETE MODELS EXHIBITING THE ALLEE EFFECT

AbstractIn this paper, we consider the discrete nonlinear delay population model exhibiting the Allee effect (*)

On the solutions of difference equations of order four

x_{n + 1} = x_n \exp \left( {a + bx_{n - \tau }^p - cx_{n - \tau }^q } \right),