Oscillation criteria for the first-order linear difference equations with several delay arguments (Q744895)

The authors establish necessary conditions for the existence of a positive solution and sufficient conditions for the oscillation of the first-order delay difference equation \[ \Delta u(k)+\sum_{i=1}^mp_i(k)\,u(\tau_i(k))=0, \] where \(p_i(k)\) are real functions and \(\tau_i:{\mathbb N}\to{\mathbb N}\) is such that \(\lim_{k\to\infty}\tau_i(k)=\infty\) for all \(i=1,\dots,m\).