Oscillatory Behavior of Linear Nonautonomous Advanced and Delayed Impulsive Differential Equations with Discontinuous Deviating Arguments via Difference Equations
Ricardo Torres Naranjo, Eugenio Trucco Vera, Özkan Öcal
Published: 2025/7/17
Abstract
We establish new sufficient conditions for the oscillatory and non-oscillatory behavior of solutions to nonautonomous advanced and delayed linear differential equations with piecewise constant arguments: $$x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in \mathbb{Z},$$ in both impulsive and non-impulsive cases (DEPCA and IDEPCA, respectively). The results rely on classical oscillation criteria for difference equations and exploit the hybrid nature of these equations, connecting them to the theory of advanced and delayed difference equations.