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2002•Journal of Jishou UniversityRequires access

The Growth of Solutions of Some Non-Homogeneous Linear Differential Equations

Jun Wang

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Abstract

In this paper,we investigate the growth of solutions of f(k)+ak-1f(k-1)+...+a1f ′-(eQ(z)-a0)f=1 (k≥1) with 1-aj(j=0,1,...,k-1) constants and Q a non-constant polynomial.It is proved that every solution f of the above equation is of order 1 and hyper order a positive interger no greater than degQ.As an application,we obtain a result on the uniqueness of meromorphic functions.

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What this paper is about

In this paper,we investigate the growth of solutions of f(k)+ak-1f(k-1)+...+a1f ′-(eQ(z)-a0)f=1 (k≥1) with 1-aj(j=0,1,...,k-1) constants and Q a non-constant polynomial.It is proved that every solution f of the above equation is of order 1 and hyper order a positive interger no greater than degQ.As an application,we obtain a result on the uniqueness of meromorphic functions.

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Available abstract

In this paper,we investigate the growth of solutions of f(k)+ak-1f(k-1)+...+a1f ′-(eQ(z)-a0)f=1 (k≥1) with 1-aj(j=0,1,...,k-1) constants and Q a non-constant polynomial.It is proved that every solution f of the above equation is of order 1 and hyper order a positive interger no greater than degQ.As an application,we obtain a result on the uniqueness of meromorphic functions.

Key concepts: Uniqueness, Meromorphic function, Mathematics, Order (exchange), Constant (computer programming), Polynomial, Homogeneous, Linear differential equation

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