Tanaka, Satoshi Oscillatory and nonoscillatory solutions of neutral differential equations. (English) Zbl 0971.34056 Ann. Pol. Math. 73, No. 2, 169-184 (2000). Consider the neutral differential equation \[ {d^n\over dt^n} \bigl[x(t)+ \lambda x(t-\tau) \bigr]+f\biggl( t,x\bigl(g(t) \bigr)\biggr) =0 \] with \(\lambda>0\), \(\tau>0\), \(g\in C([t_0,\infty))\), \(\lim_{t\to \infty} g(t)= \infty\), \(f\in C([t_0,\infty)\times\mathbb{R})\) and \(|f(t,u) |\leq F(t, |u|)\) where \(F\) is a continuous and nondecreasing function in \(u\in [0,\infty)\) for each fixed \(t\geq t_0\).Here, some sufficient conditions for the existence of oscillatory (or nonoscillatory) solutions are proved. The proofs of the main results are based on the Schauder-Tikhonov fixed-point theorem. Reviewer: Stanislaw Walczak (Łódź) Cited in 4 Documents MSC: 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations Keywords:oscillatory and nonoscillatory solutions; neutral differential equation; existence PDFBibTeX XMLCite \textit{S. Tanaka}, Ann. Pol. Math. 73, No. 2, 169--184 (2000; Zbl 0971.34056) Full Text: DOI