Asymptotic and Oscillatory Analysis of Second-Order Differential Equations with Distributed Deviating Arguments

Zuhur Alqahtani, Belgees Qaraad (), Areej Almuneef and Higinio Ramos ()
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Zuhur Alqahtani: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Belgees Qaraad: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Areej Almuneef: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Higinio Ramos: Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain

Mathematics, 2024, vol. 12, issue 22, 1-19

Abstract: This paper focuses on studying the oscillatory properties of a distinctive class of second-order advanced differential equations with distributed deviating arguments in a noncanonical case. Utilizing the Riccati method and the comparison method with first-order equations, in addition to other analytical methods, we have established criteria to test whether the solutions of the studied equation exhibit oscillatory behavior. To verify the validity of the results we obtained and determine their applicability, we present some examples to confirm the strength and accuracy of our proposed criteria.

Keywords: second-order differential equation; oscillation; nonoscillation; advanced; distributed deviating arguments (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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