Oscillation Theorems for Second‐Order Trinomial Delay‐Advance Differential Equations
Abstract
ABSTRACT We investigate the oscillatory behavior of solutions to a second‐order half‐linear differential equation involving both delayed and advanced arguments, as well as its generalization with multiple deviating arguments. The main contribution is a new iterative method that constructs sequences governing the asymptotic monotonicity properties of nonoscillatory solutions, by simultaneously incorporating both types of deviating arguments. These sequences lead to the formulation of a coupled nonlinear algebraic system whose solvability precisely characterizes the presence of nonoscillatory behavior. The resulting oscillation criteria are sharp, easily verifiable, and significantly extend and improve known results to broader classes of delay‐advance equations. Examples are given to demonstrate the sharpness of results through Euler‐type differential equations.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Mathematical and Theoretical Epidemiology and Ecology Models
Differential Equations and Numerical Methods
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Publisher
- Wiley
- Volume
- 49
- Issue
- 8
- Pages
- 8513–8531
- Publication date
- 28 January 2026
- Language
- EN