On a class of fourth-order neutral differential equation with piecewise constant arguments

Abstract

In this paper, we investigate a fourth-order neutral differential equation characterized by piecewise constant arguments. Our study focuses on establishing both the existence and uniqueness of solutions to this equation, incorporating a prescribed initial condition. In addition, we investigate the stability analysis of the above-mentioned equation and show that the zero solution of this equation cannot be asymptotically stable and indicate under what conditions it is unstable. Through rigorous mathematical analysis and theoretical exploration, this research contributes to the deeper understanding of fourth-order neutral differential equations with piecewise constant arguments, offering insights into their solution behavior and stability properties.

Keywords

• Piecewise arguments
• stability
• neutral differential equations

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