Classifying non-oscillatory solutions and oscillation of a neutral difference equation

Oscillation and Asymptotic Behaviour of Solutions of Nonlinear Two-Dimensional Neutral Delay Difference Systems

“…Case (2). The proof of case (2) is similar to that of the above theorem and hence the details are omitted.…”

“…For oscillation criteria regarding Equations (1.1)-(1.3), we refer to [2]- [12] and the references cited therein. In Section 2, we present some basic lemmas.…”

Oscillation theorems for second order nonlinear neutral difference equations

“…1 Department of Mathematics, Presidency College, Chennai, 600005, India. 2 Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, 600005, India. 3 Departmento de Ciencias Exactas e Naturais, Academia Militar, Av.…”

Classification Of Solutions Of Second Orderneutraldelay Dynamic Equations On Timescales

“…[p t (x t + h t x t − τ ) ′ ] ′ + q t x α (t − σ) = 0,(1.5) where τ and σare non-negative real numbers, and many authors (see [11]- [14]) considered various differential/difference equations, but all are studied the above equations by classifying all solutions into four classes such asM + , M − , OS and WOS and obtained criteria for the existence/non-existence of solutions in these classes.…”