Sharp conditions for the oscillation of delay difference equations

Abstract

Suppose that { p n } is a nonnegative sequence of real numbers and let k be a positive integer. We prove that urn:x-wiley:20903332:media:ista150178:ista150178-math-0001 is a sufficient condition for the oscillation of all solutions of the delay difference equation urn:x-wiley:20903332:media:ista150178:ista150178-math-0002 . This result is sharp in that the lower bound k k /( k +1) k +1 in the condition cannot be improved. Some results on difference inequalities and the existence of positive solutions are also presented.