Mohammed Al-zailah, Fahd Masood, Hamdy El-Metwall
Abstract:
This article investigates the monotonic properties and oscillatory behavior of
quasi-linear fourth-order neutral differential equations in the
noncanonical case. By establishing new monotonic properties for positive
solutions, we derive refined relationships between the solutions and their
associated auxiliary functions. Based on these results, effective
oscillation criteria are obtained to ensure the oscillation of all
solutions. The results are supported by illustrative examples and extend and
improve several existing works, and provide a useful approach for studying
more general classes of higher-order nonlinear neutral differential
equations.
Submitted January 10, 2026. Published March 30, 2026.
Math Subject Classifications: 34C10, 34K11.
Key Words: Oscillation criteria; functional differential equations; neutral equations;
quasilinear equations; fourth order; noncanonical case
DOI: 10.58997/ejde.2026.24
Show me the PDF file (365 KB), TEX file for this article.
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Mohammed Al-zailah Department of Mathematics Sana'a University P.O. Box 1247, Sana'a, Yemen email: mohamedalzayla@gmail.com |
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Fahd Masood Department of Mathematics Sana'a University P.O. Box 1247, Sana'a, Yemen email: fahdmasoud22@gmail.com |
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Hamdy El-Metwally Department of Mathematics Faculty of Science Mansoura University Mansoura 35516, Egypt email: helmetwally@mans.edu.eg |
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