Qualitative properties of some higher order difference equations

Asymptotics of Some Classes of Higher-Order Difference Equations

We present some methods for finding asymptotics of some classes of nonlinear higherorder difference equations. Among others, we confirm a conjecture posed by S. Stević (2005). Monotonous solutions of the equation yn = A + (yn−k/ ∑m j=1βj yn−qj ) p , n ∈ N0, where p,A∈ (0,∞), k,m∈N, qj , j ∈ {1, . . . ,m}, are natural numbers such that q1 < q2 < ··· < qm, βj ∈ (0,+∞), j ∈ {1, . . . ,m}, ∑m j=1βj...

Some recent global stability results for higher order difference equations ∗

We give a brief overview of some recent results for the global asymptotic stability of a difference equation xn+1 = f(n, xn, . . . , xn−k), n ≥ 0, assuming that the zero solution is the unique equilibrium. Different techniques are used, involving the use of new discrete inequalities, monotonicity arguments, and delay perturbation methods. For the particular case of linear autonomous difference ...

Some properties of algebraic difference equations of first order

Oscillation of Higher-order Delay Difference Equations

where {pi(n)} are sequences of nonnegative real numbers and not identically equal to zero, and ki is positive integer, i = 1,2, . . . , and is the first-order forward difference operator, xn = xn+1− xn, and xn = l−1( xn) for l ≥ 2. By a solution of (1.1) or inequality (1.2), we mean a nontrival real sequence {xn} satisfying (1.1) or inequality (1.2) for n ≥ 0. A solution {xn} is said to be osci...

Difference Equations in Massive Higher Order Calculations

The calculation of massive 2–loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter N. We report on the solution of these sums through higher order difference equations using the summatio...