Oscillation Solutions for Nonlinear Second-Order Neutral Differential Equations

Omar Bazighifan (), Nawa Alshammari, Faten Aldosari and Loredana Florentina Iambor ()
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Omar Bazighifan: Department of Mathematics, Faculty of Science, Seiyun University, Hadhramout 50512, Yemen
Nawa Alshammari: Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
Faten Aldosari: Department of Mathematics, College of Science, Shaqra University, P.O. Box 15572, Shaqra 11961, Saudi Arabia
Loredana Florentina Iambor: Department of Mathematics and Computer Science, University of Oradea, University Street, 410087 Oradea, Romania

Mathematics, 2025, vol. 13, issue 2, 1-17

Abstract: This research investigates the oscillation criteria of nonlinear second-order neutral differential equations with multiple delays, focusing on their noncanonical forms. By leveraging an innovative iterative technique, new relationships are established to enhance the monotonic properties of positive solutions. These advancements lead to the derivation of novel oscillation criteria that significantly extend and refine the existing body of knowledge in this domain. The proposed criteria address gaps in the literature, providing a robust framework for analyzing such differential equations. To demonstrate their practical implications, three illustrative examples are presented, showcasing the applicability and effectiveness of the results in solving real-world problems involving delay differential equations.

Keywords: oscillation criteria; neutral differential equations; multiple delays; noncanonical forms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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