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

Shyam Sundar Santra, Abhay Kumar Sethi, Osama Moaaz, Khaled Mohamed Khedher and Shao-Wen Yao
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Shyam Sundar Santra: Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India
Abhay Kumar Sethi: Department of Mathematics, Sambalpur University, Sambalpur 768019, India
Osama Moaaz: Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
Khaled Mohamed Khedher: Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
Shao-Wen Yao: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

Mathematics, 2021, vol. 9, issue 10, 1-11

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 ) G 1 ( v ( κ ( ξ ) ) ) + d ( ξ ) G 2 ( v ( ς ( ξ ) ) ) = 0 under canonical and non-canonical operators, that is, ∫ ξ 0 ∞ d ξ a ( ξ ) = ∞ and ∫ ξ 0 ∞ d ξ a ( 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.

Keywords: differential equations; second-order; neutral; delay; oscillation criteria (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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