Oscillation theorems for second-order nonlinear neutral differential equations

Oscillation of Sublinear and Superlinear Second Order Neutral Differential Equations

“…In this work, an attempt is to study (1) such that G and H could be strictly sublinear or superlinear. We note that not only the present work generalizes the work of [4], but also it generalizes the work of [2] and [3]. The neutral differential equations find numerous applications in natural sciences and technology.…”

Oscillation Criteria for Second‐Order Neutral Damped Differential Equations with Delay Argument

“…(1), i.e., when pðtÞ¼0 (for example, see Refs. [8][9][10][11][12][13][14][15][16][17][18]). For instance, in one of the pioneering works on the subject, Grammatikopoulos et al [8] studied the second-order neutral differential equation with constant delay of the form…”

“…(1) and by defining a sequence of continuous functions has obtained various kinds of better results. Afterward, his approach has been further developed by several authors, see, e.g., [11][12][13][14]. However, it appears that very little is known regarding the oscillation of Eq.…”

Oscillation of Second-Order Neutral Differential Equations

“…A solution of (1) Li et al [14] studied oscillation of equation (1) under the assumptions that (2) holds, t and s are strictly increasing, pðtÞ > 1, and (4) is satisfied. Li et al [15] analyzed oscillatory properties of equation (1) in the case where ðH 1 Þ-ðH 3 Þ hold, tðtÞ b t, and sðtÞ b t: They derived a su‰cient condition which ensures that solutions of equation (1) We stress that theorems in [4,5,6,11] cannot be applied to (1) in the case where (2) holds. The purpose of this paper is to extend a new method for the analysis of the oscillation of equation (1) via comparison principles suggested by Baculíková and Džurina [4] for the study of (1) under the assumption (2).…”