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Content available remote Global behavior of higher order a rational difference equation
Elabbasy E.M., Eleissawy S M
Fasciculi Mathematici
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2014
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Nr 53
39--52
EN
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.
2
Content available remote Qualitative properties for a higher order rational difference equation
Elabbasy E.M., Eleissawy S M
Fasciculi Mathematici
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2013
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Nr 50
33--50
EN
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.
3
Content available Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments
Elabbasy E. M., Hassan T. S., Moaaz O.
Opuscula Mathematica
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2012
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Vol. 32, no. 4
719-730
EN
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.
4
Content available Oscillation theorems concerning non-linear differential equations of the second order
Elabbasy E.M., Elzeiny Sh.R.
Opuscula Mathematica
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2011
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Vol. 31, no. 3
373-391
EN
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.
5
Content available remote On the solution of the recursive sequence
Elabbasy E.M., Elsayed E.M.
Fasciculi Mathematici
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2009
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Nr 41
55-63
EN
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.
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