Corrigendum Corrigendum to " WKB (Liouville–Green) analysis of second order difference equations and applications " [J. There is a hypothesis which is missing from Theorem 2.3 in the above article [1]. The line above Eq. (2.34). 'For N 1 infinite assume that (2.30) and (2.31) hold for all n ≥ N , that' should read 'For N 1 infinite assume that (2.30) and (2.31) hold for all n ≥ N , that for eac...

To better understand the evolution of dispersal in spatially heterogenous landscapes, we study difference equation models of populations that reproduce and disperse in a landscape consisting of k patches. The connectivity of the patches and costs of dispersal are determined by a k × k column substochastic matrix S where Sij represents the fraction of dispersing individuals from patch j that end...

We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies conti...

In this paper, some criteria for the oscillation of the high order partial difference equations of the form T i(xm,n+axm−k1,n−l1−bxm+k2,n+l2) = c(qxm−σ1,n−τ1+pxm+σ2,n+τ2) are established, where c = ±1, i ∈ N = {1, 2, 3, . . .}.

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).