Oscillatory behavior of \(n^{th}\)-order neutral differential equations with continuous deviating arguments
The paper deals with the \(n\)th-order neutral functional-differential equation \[ [a(t)[x(t)| x(t)|^{\alpha-1}+p(t)x(\tau(t))]^{(n-1)}]'+\delta\int_c^d q(t,\xi)f(x(\sigma(t,\xi)))\,d\xi =h(t),\tag{1} \] with \(\delta=\pm 1\), \(t\geq 0\). The author presents sufficient conditions for equation (1) to be almost oscillatory in the sense that every solution \(x(t)\) of this equation is either oscillatory or else \(\lim_{t\to\infty}| x(t)| =\infty\), or \(\liminf_{t\to\infty}| x(t)| =0\). Two examples are given for illustration.
scientific article; zbMATH DE number 2167467