Comparison and oscillation results for difference equations with continuous variable (Q5931829)

The author establishes comparison theorems for the oscillation of all solutions of the difference equation with continuous variable \[ x(t)-x(t-\tau)+\sum_{i=1}^n \left[p_i(t)x(t-\sigma_i)-q_i(t)x(t-r_i)\right]=0.\tag \(*\) \] Some explicit sufficient conditions for the oscillation of all solutions to \((*)\) are also obtained by using the comparison theorems and the well-known oscillation results on delay differential equations. For related results see the paper of the author [Chin. Sci. Bull. 41, No. 18, 1506-1510 (1996; Zbl 0867.39005)].