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Differential polynomials generated by second order linear differential equations

Belaidi B., El Farissi A.

Journal of Applied Analysis

2008

Vol. 14, nr 2

259-271

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.