Asymptotic analysis of ODEs (Q1919433)

The authors consider the oscillatory and asymptotic behaviour of ordinary differential equations of the form \[ \Biggl({1\over r_{n-1}(t)}\cdots\Biggl({1\over r_1(t)} y'(t)\Biggr)'\cdots\Biggr)'+p(t) y(t)=0,\tag{1} \] where \(n\geq2\) and (i) \(p,r_i\in C((t_0,\infty),(0,\infty))\), \(1\leq i\leq n-1\), (ii) \(\int^\infty_{t_0} r_i(s)ds=\infty\) for \(1\leq i\leq n-1\). In the paper, the behaviour of solutions of (1) is deduced by comparing this equation with a set of first-order advanced differential inequalities.