Note on the oscillation of certain difference equations

Błaz̄ej Szmanda, Poznań, Poland

AMS Subject classification: 39A10

Keywords: oscillation, nonoscillatory solution, difference equations

Abstract: The nonlinear difference equation of the form Δ^{m}u(n) + a(n)f(u(r(n))) = 0, m ≥ 2, n ∈ N is considered, where Δ^{m} is the m-th order forward difference operator, a : N → [0, ∞), r : N → Z, f : R → R and uf(u) > 0 for u ≠ 0. Some new criteria for the oscillatory and asymptotic behavior of solutions of the above equation are given.