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2002•Bulletin of the Australian Mathematical SocietyOpen access

On meromorphic solutions of certain nonlinear differential equations

Janne Heittokangas, Risto Korhonen, Ilpo Laine

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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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What this paper is about

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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OpenAlex reports 31 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Meromorphic function, Mathematics, Uniqueness, Polynomial, Complement (music), Nonlinear system, Function (biology), Differential (mechanical device)

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