Journal of Applied Analysis Vol. 14, No. 2 (2008), pp. 259–271 DIFFERENTIAL POLYNOMIALS GENERATED BY SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS B. BELA ¨ IDI and A. EL FARISSI Received December 5, 2007 and, in revised form, July 14, 2008 Abstract. In this paper, we study fixed points of solutions of the dif- ferential equation f ′′ + A 1 (z) f ′ + A 0 (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. 1. Introduction and main results Throughout this paper, we assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna’s value distribution theory and with the basic Wiman Valiron theory as well (see 2000 Mathematics Subject Classification. Primary: 34M10, 30D35. Key words and phrases. Linear differential equations, meromorphic solutions, hyper order, exponent of convergence of the sequence of distinct zeros, hyper exponent of con- vergence of the sequence of distinct zeros. ISSN 1425-6908 c  Heldermann Verlag.