Oscillation and nonoscillation of a class of functional equations (Q2747576)

Here, the following equation NEWLINE\[NEWLINEx(g(t))=p(t)x(t)+\sum\limits_{i=1}^{m}Q_i(t)x(g^{k+i}(t))NEWLINE\]NEWLINE is considered, with \(Q_i : I\rightarrow \mathbb{R}=(0, \infty)\), \(i=1,2,\ldots, m\), \(I\subset (0, \infty)\) an unbounded set, \(g : I \rightarrow I\), \(g(t)\not\equiv t\), \(\lim_{t\rightarrow\infty}g(t)=\infty\), \(t\in I\), \(k \geq 1\) a positive integer. Some oscillation and nonoscillation criteria are obtained.