Oscillation of solutions of neutral delay differential equations
Here, the first-order neutral equation \[ \biggl(x(t)-p(t)x \bigl(g(t)\bigr) \biggr)'+Q(t)x \bigl(h(t) \bigr)=0\tag{1} \] is considered, with \(P,Q\in C([a,\infty); \mathbb{R}^+)\); \(g,h\in C([a,\infty), \mathbb{R})\), \(\lim_{t\to \infty} g(t)=\lim_{t\to\infty} h(t)=\infty\), \(g(t)<t\), where \(t\in [a,\infty)\). Sufficient conditions for the oscillation of all solutions to (1) are established.
scientific article; zbMATH DE number 1545780