Work

Improved Solution–Function Inequalities and Kneser-Type Oscillation Criteria for Noncanonical Neutral Differential Equations with Continuous Delay

Year: 2026

Type: article

Abstract: This paper investigates the oscillatory behavior of second-order noncanonical neutral differential equations involving a neutral term with continuous delay and distributed deviating arguments. The main contribution is the establishment of a new and sharper relation between the solution and the corresponding neutral function, a problem that has not been addressed previously for noncanonical neutral equations with continuous delay. By combining iterative techniques with refined inequalities, we derive several new oscillation criteria, including Kneser-type conditions. The obtained results significantly extend the existing theory and improve a number of known oscillation tests in the literature. Illustrative examples and detailed comparisons with recent criteria demonstrate the effectiveness and superiority of the proposed approach in detecting oscillatory solutions.

Source: Axioms

DOI: 10.3390/axioms15110799

Authors: Osama Moaaz, Asma Al-Jaser

Institutions: Qassim University, Mansoura University, Princess Nourah bint Abdulrahman University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Princess Nourah Bint Abdulrahman University