Differential polynomials generated by second order linear differential equations

Abstract

In this paper, we study fixed points of solutions of the differential equation f+ A1 (z) f+ A0 (z) f= 0, where Aj (z)(≡ 0)(j= 0, 1) are transcendental meromorphic functions with finite order. Instead of looking at the zeros of f (z)− z, we proceed to a slight generalization by considering zeros of g (z)− ϕ (z), where g is a differential polynomial in f with polynomial coefficients, ϕ is a small meromorphic function relative to f, while the solution f is of infinite order.