Abstract:

The oscillation of a class of second order nonlinear neutral variable delay difference equation with positive and negative coefficients is discussed. Using the fixed point theorem in Banach space, a new nonoscillation criteria for the equation is obtained by introducing parameter function and the generalized Riccati transformation. Also, a sufficient condition for oscillation of the equation is proposed. These criteria can improve the restriction of the conditions for the equation, which promote some existed results.

Key words: positive and negative coefficient; neutral difference equation; variable delay; nonlinear; oscillation and nonoscillation; Riccati transformation