Journal of the
Korean Mathematical Society JKMS

Quadratic invariant curve is one of the simplest nonlinear invariant curves and was considered by C. T. Ng and the author in order to study the one-dimensional nonlinear dynamics displayed by a second order delay di?erential equation with piecewise constant argument. In this paper a functional equation derived from the problem of invariant curves is discussed. Using a di?erent method from what C. T. Ng and the author once used, we de?ne solutions piecewisely and give results in the remaining di?cult case left in C. T. Ng and the author’s work. A problem of analytic extension given in their work is also answered negatively.

Keywords: functional equation, invariant curve, de?ning piecewisely, divergence