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

Authors :: Shyam Sundar Santra
Abhay Kumar Sethi
Shao-Wen Yao
Osama Moaaz
Khaled Mohamed Khedher
Source :: Mathematics, Vol 9, Iss 1111, p 1111 (2021), Mathematics, Volume 9, Issue 10
Publication Year :: 2021
Publisher :: MDPI AG, 2021.
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)&lt<br />∞. 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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