Oscillatory solutions of linear iterative functional equations
The authors give three sufficient conditions for the oscillation of all solutions \(x\) of the linear functional equation \[ Q_0(t)x(t)+Q_1(t)x(g(t))+Q_2(t)x(g^2(t))+\dots +Q_{m+1}(t)x(g^{m+1}(t))=0, \] where \(m\) is a fixed positive integer, the functions \(Q_k:I\to \mathbb{R}\) for \(k\in \{0, \dots , m+1\}\), \(g:I\to I\) are given and \(I\) is an unbounded subset of the set of positive reals. These conditions can be applied to recurrence equations if one takes the set of positive integers as \(I\). Moreover, the authors compare their results with known results for the recurrence equation \[ \Delta x(n)=p(n)x(n+2), \] where \(p:\mathbb{N}\to (0,\infty)\).
scientific article; zbMATH DE number 2141194