A generalization of Elsayed's solution to the difference equation x n + 1 = x n − 5 − 1 + x n − 2 x n − 5

The Behaviour of the Positive Solutions of the Difference Equation x n = A + ( x n − 2 x n − 1 ) p Kenneth

This paper studies the boundedness, global asymptotic stability and periodicity for solutions of the equation xn = A + ( xn−2 xn−1 )p , n = 0, 1, . . . , with p, A ∈ (0,∞), p 6= 1, and x−2, x−1 ∈ (0,∞). It is shown that: (a) all solutions converge to the unique equilibrium, x̄ = A+1, whenever p ≤ min{1, (A+1)/2}, (b) all solutions converge to period two solutions whenever (A + 1)/2 < p < 1 and (...

The Nature of Halogen Bonds in [N∙∙∙X∙∙∙N]+ Complexes: A Theoretical Study

     The effects of substituents on the symmetry and the nature of halogen bonds in [N∙∙∙X∙∙∙N]+-type systems are presented for the YC5H4N∙∙∙X∙∙∙NC5H5 (Y = NO2, CN, H, CH3, OCH3, OH, NH2, X = Cl, Br, I) complexes. Some structural parameters, energy data and electronic properties were explored with...

On the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

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...

” THE DIOPHANTINE EQUATION x n = Dy 2 + 1 ”