where Δ is the forward difference operator Δxn = xn+1 − xn, Δxn = Δ(Δxn), φp(s) is p-Laplacian operator φp(s) = |s|p−2s (1 < p < ∞), and f : Z×R3 → R is a continuous functional in the second, the third, and fourth variables and satisfies f (t +m,u,v,w) = f (t,u,v,w) for a given positive integerm. We may think of (1.1) as being a discrete analogue of the second-order functional differential equa...

It is shown how to define difference equations on particular lattices {xn}, n ∈ Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.

We show on the example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial Leibniz rule suitable to find the symmetries of discrete equations. In this way we obtain a symmetry Lie algebra, defined in terms of shift operators, isomorphic to that of the continuous heat equation.

In this paper a sufficient condition is obtained for the global asmptotic stability of the following system of difference equations zn+1 = tn + zn−1 tnzn−1 + a , tn+1 = zn + tn−1 zntn−1 + a , n = 0, 1, 2, ... where the parameter a (0,∞) and the initial values (zk, tk) (0,∞) (for k = −1, 0).

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distribu...

In this paper we consider the oscillation of the delay difference equation with oscillating coefficients x,,+l x. + 2p,(n):z’._k.. 0, n 0. Some comparison and oscillation results are obtained.

In this communication a general kind of simplex partitions are studied. These partitions are associated to some recurrence relations. The study of these equations lead us to set some properties in 2D and 3D about the average adjacencies of the topological entities defining the mesh, when the number of refinements tends to infinite. We prove that this limit is independent of the considered parti...

By means of Riccati transformation technique, we establish some new oscillation criteria for second-order nonlinear delay difference equation ∆(pn (∆xn) ) + qnf(xn−σ) = 0, n = 0, 1, 2, . . . ,

Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether’s Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not d...