On almost oscillation of functional differential equations with deviating arguments (Q788888)

In this paper we are particularly interested in the situation in which the differential equation with a parameter (1) \(x^{(n)}(t)\pm \lambda p(t)x(g(t))=0\) is almost oscillatory for all \(\lambda>0\). We obtain first sufficient conditions and then necessary conditions for (2) \(x^{(n)}(t)+\sigma p(t)x(g(t))=0\), \(\sigma =\pm 1\), \(n\geq 2\) to be almost oscillatory, and, finally, combine them to give, under suitable conditions on the deviating argument g(t), a characterization for the situation in which (1) is almost oscillatory for all \(\lambda>0\).