Oscillation of \(n\)th order strongly noncanonical delay differential equations
In this paper, the \(n\)th order delay differential equation \[ (r_{n-1}(t) (r_{n-2}(t) \cdots (r_1(t)y'(t))' \cdots )')' + p(t) y(\tau(t)) = 0, \quad t \ge t_0 \] is considered, where \(n \ge 2\), \(r_i \in C[t_0,\infty)\), \(r_i(t)>0\) for \(t\ge t_0\), \(\int_{t_0}^\infty 1/r_i(s)ds<\infty\) for \(i=1\), \(2\), \(\cdots\), \(n-1\), \(p \in C[t_0,\infty)\), \(p(t)>0\) for \(t\ge t_0\), \(\tau \in C[t_0,\infty)\), \(\tau(t)\le t\) for \(t\ge t_0\), and \(\tau(t)\to\infty\) as \(t\to\infty\). Sufficient conditions for every solution to be oscillatory are derived.
scientific article; zbMATH DE number 7317512