Oscillatory behavior of solutions of Volterra summation equations

Abstract Sufficient conditions for the oscillation of solutions of (E1) Y n =p n + ∑ s=0 n−1 L(n,s)g(y s ), n∈ N and (E2) Y n =p n − ∑ s=0 n−1 K(n,s,y s −l), n∈ N are obtained. Here, {pn} is a sequence, D; ∈ N = {0, 1, 2, …} , L(n, s) > 0, for n ≥ s ∈ N , and L(n, s) =0, if n 0, for u ≠ 0, Φ → K(n, s, Φ) maps bounded sets into bounded sets, and for all (n, s) ∈ N × N , ΦK(n, s, Φ) ≥ 0 if Φ ≠ 0.