Asymptotic and Oscillatory Analysis of Fourth-Order Nonlinear Differential Equations with p -Laplacian-like Operators and Neutral Delay Arguments

Mansour Alatwi, Osama Moaaz (), Wedad Albalawi (), Fahd Masood and Hamdy El-Metwally
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Mansour Alatwi: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Osama Moaaz: Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
Wedad Albalawi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Fahd Masood: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Hamdy El-Metwally: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2024, vol. 12, issue 3, 1-23

Abstract: This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their corresponding functions and derivatives. By refining these relationships, we unveil new insights into the asymptotic properties governing these solutions. These insights lead to the establishment of improved conditions that ensure the nonexistence of any positive solutions to the studied equation, thus obtaining improved oscillation criteria. In light of the broader context, our findings extend and build upon the existing literature in the field of neutral differential equations. To emphasize the importance of the results and their applicability, this paper concludes with some examples.

Keywords: nonlinear differential equations; asymptotic and oscillatory analysis; fourth-order; p -Laplacian-like operators; neutral delay arguments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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