On the oscillatory properties of the solutions of a class of integro- differential equations of neutral type (Q1186340)

The oscillatory properties of the solutions to the integrodifferential equation \([(Lx)(t)]^{(n)}+\int_{I_ t}K(t,s,x(s))ds=0\) is considered, where \(L\) is an operator of difference type, \(n\geq 1\), \(I_ t\subset R\), \(K:D_ K\to R\), \(D_ K\subseteq R^ 3\), \(x:[\alpha_ x,\infty]\to R\). It is shown that for \(n\) even all ultimately nonzero solutions oscillate and for \(n\) odd they either oscillate or tend to zero as \(t\to \infty\). This is an extension of the authors previous results.