Holomorphic solutions to pantograph type equations with neutral fixed points (Q596751)

The authors mainly consider a generalization of the pantograph equation \[ y'(z)+ by(z)-\lambda y(g(z))= 0, \] where \(b\) and \(\lambda\) are complex constants with \(\lambda\neq 0\), and \(g\) is an entire function with a fixed-point at \(z= z_0\). \textit{J. C. W. Rogers} [IMA J. Appl. Math. 41, No. 2, 105--134 (1988; Zbl 0687.34053)] and \textit{B. van Brunt} [N. Z. J. Math. 22, No. 1, 101--107 (1993; Zbl 0783.34052)] studied coupled systems of nonlinear functional-differential equations, that include above equation as a special case.