Asymptotic behaviour of a class of nonlinear functional differential equations of third order (Q5938922)

The authors consider the third-order nonlinear delay differential equation NEWLINE\[NEWLINEy'''(t)+ p(t) y'(t)+ q(t) F(y(g(t)))= 0,NEWLINE\]NEWLINE with \(p,q\in C([a,\infty), \mathbb{R})\), \(g\in C([a, \infty),\mathbb{R})\), \(0< g(t)\leq t\) for \(t\geq a\), \(g(t)\to \infty\) as \(t\to\infty\) and \(F\in C(\mathbb{R}, \mathbb{R})\) satisfies \(F(u)/u\geq \beta> 0\) for \(u\neq 0\). Sufficient conditions are given under which every nonoscillatory solution tends either to zero or to \(\pm\infty\).