Existence and uniqueness of periodic solutions for a delay differential equation with piecewise constant arguments
The aim of this paper is to establish sufficient conditions for the existence and uniqueness of \(T\)-periodic solution of the following delay differential equation with piecewise constant argument: \[ \dot{x}(t)+f(t,x(t-h),x([t-k]))=0, \] where \(h\) and \(k\) are integers, \([\cdot]\) denotes the greatest-integer function, \(f\in C(\mathbb{R}^3;\mathbb{R})\), and \(f(t+T,u,v)=f(t,u,v)\) for \((t,u,v)\in \mathbb{R}^3\). The main tool is Mawhin's continuation theorem. However, the main result is independent of the two delays and the fact of piecewise constant arguments.
scientific article; zbMATH DE number 5535146