Oscillation criteria of first-order linear difference equations with delay argument (Q2470092)

The authors present new sufficient conditions for the oscillation of all proper solutions of the first-order linear difference equation with delay argument \[ \Delta u(k)+p(k)u(\tau(k))=0,\quad k\in N, \] where \(\Delta u(k)=u(k+1)-u(k)\), \(p:\mathbb N\to\mathbb R_+\), \(\tau:\mathbb N\to\mathbb N\) and \(\lim_{k\to +\infty}\tau(k)=+\infty\). Examples illustrating the results are given.