Oscillation criteria for certain third order nonlinear difference equations

Some new criteria for the oscillation of all solutions of third order nonlinear difference equations of the form ∆ (a(n)(∆2 x(n))α + q(n)f (x[g(n)]) = 0 and ∆ (a(n)(∆2 x(n))α = q(n)f (x[g(n)]) + p(n)h(x[σ(n)]) ∞ -1/α with P a (n) < ∞ are established.