Oscillations of difference equations with several delays

Consider the first-order delay difference equation where lim infn→∞ Pi(n) = pi ≥ 0, ki > 0, i = 1,2,… Sufficient conditions for the oscillation of all solutions of the above equation are established in the case when the corresponding “limiting” equation admits nonoscillatory solutions. Oscillation criteria for the nonlinear difference equation are also derived as applications.