New Asymptotic and Oscillatory Results for Third-Order Noncanonical Advanced Differential Equations

Asma Althemairi, Stefano Serra-Capizzano (), Belgees Qaraad and Higinio Ramos
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Asma Althemairi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Stefano Serra-Capizzano: Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100 Como, Italy
Belgees Qaraad: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Higinio Ramos: Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain

Mathematics, 2025, vol. 13, issue 15, 1-19

Abstract: The aim of this study is to investigate the oscillatory behaviour of a new class of third-order advanced differential equations in their noncanonical form. By employing newly refined transformations, the noncanonical equation is converted into its canonical form. This transformation reduces the number of possible nonoscillatory solution categories from four to two. The present study is based on a thorough and comprehensive review of existing literature and introduces new oscillation criteria by the comparison principle and other analytical techniques. These criteria provide sufficient conditions for the oscillation of solutions without imposing additional restrictive assumptions. The validity and significance of the obtained results are demonstrated through illustrative examples.

Keywords: oscillation; third-order; noncanonical; advanced differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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