Shen, J. H.; Stavroulakis, I. P.; Tang, X. H. Hille-type oscillation and nonoscillation criteria for neutral equations with positive and negative coefficients. (English) Zbl 1051.34053 Stud. Univ. Žilina, Math. Ser. 14, No. 1, 45-59 (2001). Summary: Hille-type oscillation and nonoscillation criteria are established for the neutral differential equation with positive and negative coefficients \[ \bigl[x(t)- R(t)x(t-r)\bigr]'+ P(t)x(t-\tau)-Q(t)x(t-\sigma)= 0,\;t\geq t_0, \] with \(r\in(0,\infty)\), \(\tau,\sigma\in [0,\infty)\), \(P,Q,R \in C([t_0,\infty), \mathbb{R}^+)\). These criteria essentially improve many known oscillation results in the literature. Necessary and sufficient conditions for the existence of bounded positive solutions and sufficient conditions for the existence of unbounded positive solutions are obtained, too. Cited in 6 Documents MSC: 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations PDFBibTeX XMLCite \textit{J. H. Shen} et al., Stud. Univ. Žilina, Math. Ser. 14, No. 1, 45--59 (2001; Zbl 1051.34053)