New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation

Abstract

In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form (a(ξ)((v(ξ)+b(ξ)v(ϑ(ξ)))′))′+c(ξ)G1(v(κ(ξ)))+d(ξ)G2(v(ς(ξ)))=0 under canonical and non-canonical operators, that is, ∫ξ0∞dξa(ξ)=∞ and ∫ξ0∞dξa(ξ)<∞. We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results.

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“…Recently, there has been a remarkable development in the study of the oscillatory behavior of solutions of functional differential equations of different orders and of different types, such as equations with delay, neutral and advanced equations, as well as equations that include a middle term that includes damping. Second-order delay equations have been the subject of interest and development in [10][11][12]. Refs.…”

Oscillatory Properties of Third-order Neutral Delay Difference Equations

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Application of Fourier Transform to Study Hyers-Ulam Stability of Linear Differential Equations

“…where a is a four times continuously differentiable function, h, f, u and g are scalars and ξ(e) is the continuously differentiable function. There are many related works [12][13][14][15][16][17][18][19] and the reference references cited therein. The outline of the paper as follows: In Section 2, some definitions are introduced.…”