On the growth of meromorphic and entire solutions of second-order algebraic differential equations

In this paper, the growth of the meromorphic solutions of the equation where L, M, N are birational functions, is studied. We prove that if L(z, f) satisfies a quite general condition, then f must be of finite order. Furthermore, if (L(z, f)≡0, and M(z, f), N(z, f) are polynomials in f, then the order of any entire solution of the equation is a positive integral multiple of 1/2. Entrata in Redazione il 15 marzo 1999. The research was partially supported by a UGC grant of Hong Kong (Project No: HKUST 712/96p).