Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations

Hail S. Alrashdi, Wedad Albalawi (), Ali Muhib, Osama Moaaz and Elmetwally M. Elabbasy
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Hail S. Alrashdi: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Wedad Albalawi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Ali Muhib: 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
Elmetwally M. Elabbasy: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2024, vol. 12, issue 11, 1-16

Abstract: This paper aims to study the asymptotic properties of nonoscillatory solutions (eventually positive or negative) of a class of third-order canonical neutral differential equations. We use Riccati substitution to reduce the order of the considered equation, and then we use the Philos function class to obtain new criteria of the Kamenev type, which guarantees that all nonoscillatory solutions converge to zero. This approach is characterized by the possibility of applying its conditions to a wider area of equations. This is not the only aspect that distinguishes our results; we also use improved relationships between the solution and the corresponding function, which in turn is reflected in a direct improvement of the criteria. The findings in this article extend and generalize previous findings in the literature and also improve some of these findings.

Keywords: quasi-linear differential equations; asymptotic and oscillatory analysis; third-order; neutral delay arguments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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