Property $ \bar{A} $ of third-order noncanonical functional differential equations with positive and negative terms

S. Sangeetha; S. K. Thamilvanan; S. S. Santra; S. Noeiaghdam; M. Abdollahzadeh; S. Sangeetha; S. K. Thamilvanan; S. S. Santra; S. Noeiaghdam; M. Abdollahzadeh

doi:10.3934/math.2023724

AIMS Mathematics

2023, Volume 8, Issue 6: 14167-14179. doi: 10.3934/math.2023724

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Research article

Property $ \bar{A} $ of third-order noncanonical functional differential equations with positive and negative terms

1.
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India
2.
Department of Mathematics, JIS College of Engineering, Kalyani, Nadia, West Bengal 741235, India
3.
Department of Mathematics, Applied Science Cluster, University of Petroleum and Energy Studies, Dehradun, Uttarakhand 248007, India
4.
Department of Applied Mathematics and Programming, South Ural State University, Lenin prospect 76, Chelyabinsk 454080, Russia
5.
School of Information Technology and Data Science, Irkutsk National Research Technical University, Irkutsk 664074, Russia
Correction on: AIMS Mathematics 9: 8803–8804.

Received: 03 January 2023 Revised: 28 February 2023 Accepted: 14 March 2023 Published: 17 April 2023
MSC : 34C10, 34K11

In this article, we have derived a new method to study the oscillatory and asymptotic properties for third-order noncanonical functional differential equations with both positive and negative terms of the form

$ \begin{equation*} (p_2 (t)(p_1 (t) x'(t) )')'+a(t)g(x(\tau(t)))-b(t)h(x(\sigma(t)) = 0 \end{equation*} $

Firstly, we have converted the above equation of noncanonical type into the canonical type using the strongly noncanonical operator and obtained some new conditions for Property $ \bar{A} $. We furnished illustrative examples to validate our main result.
- Property $ \bar{A} $,
- third-Order,
- noncanonical,
- delay argument
Citation: S. Sangeetha, S. K. Thamilvanan, S. S. Santra, S. Noeiaghdam, M. Abdollahzadeh. Property $ \bar{A} $ of third-order noncanonical functional differential equations with positive and negative terms[J]. AIMS Mathematics, 2023, 8(6): 14167-14179. doi: 10.3934/math.2023724

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Abstract

In this article, we have derived a new method to study the oscillatory and asymptotic properties for third-order noncanonical functional differential equations with both positive and negative terms of the form

$ \begin{equation*} (p_2 (t)(p_1 (t) x'(t) )')'+a(t)g(x(\tau(t)))-b(t)h(x(\sigma(t)) = 0 \end{equation*} $

Firstly, we have converted the above equation of noncanonical type into the canonical type using the strongly noncanonical operator and obtained some new conditions for Property $ \bar{A} $. We furnished illustrative examples to validate our main result.

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