On meromorphic solutions of certain nonlinear differential equations

2002/10/01 by J. Heittokangas, Janne Heittokangas, R. Korhonen +3 · 1 citation
Mathematics · #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.1017/s000497270004017x

Abstract

In this paper, we consider the growth of meromorphic solutions of nonlinear differential equations of the form L ( f ) + P ( z , f ) = h ( z ), where L ( f ) denotes a linear differential polynomial in f , P ( z , f ) is a polynomial in f , both with small meromorphic coefficients, and h ( z ) is a meromorphic function. Specialising to L ( f ) − p ( z ) f n = h ( z ), where p ( z ) is a small meromorphic function, we consider the uniqueness of meromorphic solutions with few poles only. Our results complement earlier ones due to C.-C. Yang.

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