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Global behavior of higher order a rational difference equation

100%

Elabbasy E. M. , Eleissawy S. M.

Fasciculi Mathematici

2014

tom Nr 53

39--52

The main objective of this paper is to study the global asymptotic stability and the periodic character of the rational difference equation …[wzór], n – 0,1,…, where the parameters a, β, ϒ, p, q are nonnegative real numbers and initial conditions are nonnegative real numbers l, r, k are nonnegative integers, such that l < k and r < k. Also, we give some numerical simulations to the equation to illustrate our results.

Qualitative properties for a higher order rational difference equation

100%

Elabbasy E. M. , Eleissawy S. M.

Fasciculi Mathematici

2013

tom Nr 50

33--50

The main objective of this paper is to study the behavior of solutions of the difference equation ...[wzór] where the initial conditions x-r, x-r+1,...,x0 are arbitrary positive real numbers, r = max{q, l,p} is nonnegative integer and a, b, c, d are positive constants. Also, we give the solution of some special cases of this equation.

Oscillation theorems concerning non-linear differential equations of the second order

100%

Elabbasy E. M. , Elzeiny S. R.

Opuscula Mathematica

2011

tom Vol. 31, no. 3

373-391

This paper concerns the oscillation of solutions of the differential eq. [r,(t) ψ(x(t)) ƒ (x(t))] + q(t) φ (g(x(t)), r(t)ψ(x(t))=0 where uφ(u,v) > 0 for all u ≠ 0, xg(x)>0, xf(x)>0 for all x ≠ 0, ψ(x)>0 for all x ∈ R, r(t)>0 for t≥t0>0 and q is of arbitrary sign. Our results complement the results in [A.G. Kartsatos, On oscillation of nonlinear quations of second order, J. Math. Anal. Appl. 24 (1968), 665-668], and improve a number of existing oscillation criteria. Our main results are illustrated with examples.

On the solution of the recursive sequence

100%

Elabbasy E. M. , Elsayed E. M.

Fasciculi Mathematici

2009

tom Nr 41

55-63

We obtain in this paper the solution of the following recursive sequence where the initial conditions x-2, x-1are arbitrary non zero real numbers.

Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments

80%

Elabbasy E. M. , Hassan T. S. , Moaaz O.

Opuscula Mathematica

2012

tom Vol. 32, no. 4

719-730

Oscillation criteria are established for second order nonlinear neutral differential equations with deviating arguments of the form [formula] where α > 0 and z(t) = x(t) + p(t)x(t - ϒ). Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results.