Comparison theorems for the oscillation of difference equations with continuous arguments and applications (Q674657)

Consider the difference equation with continuous arguments \[ y(t)- y(t-\tau)+ \sum^\infty_{i=1} p_i(t)y(t-\sigma_i)=0,\tag{1} \] \[ y(t)- y(t-\tau)+ p(t)y(t-\sigma)=0,\tag{2} \] where \(\tau\), \(\sigma\) and \(\sigma_i\) are positive constants, \(p_i(t)\) and \(p(t)\in C(R^+,R^+)\). In this note, the author compares equation (1) with certain delay differential equation, and thereby establishes some new sufficient conditions for the oscillation of equations (1) and (2).