Asymptotic behaviour of solutions of third order delay-differential equations. (English) Zbl 1025.34068

The authors consider the asymptotic behaviour of the solutions to the third-order delay differential equation \[ y'''(t)+ c(t)y\bigl(g(t) \bigr) =0, \tag{1} \] with \(g\in C([\sigma, \infty),\mathbb{R})\), \(g(t)\leq t\) and \(\lim_{t\to \infty} g(t)=\infty\). More precisely, they study the so-called properties \(A\) and \(B\). In the process, sufficient conditions for oscillation of all solutions to (1) are obtained. Unlike, most of the papers in which the behaviour of (1) is investigated with the help of certain nondelay equations, the authors study the properties \(A\) and \(B\) of (1) directly.
Reviewer: V.Petrov (Plovdiv)


34K11 Oscillation theory of functional-differential equations