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2014•Journal of Jiangxi Normal UniversityRequires access

The Growth of Solutions of a Class of Higher Order Complex Differential Equations

Gong Pa

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Abstract

The growth of solutions of the higher order linear differential equations f( k)+ ∑j = 1Pj( e-z) f( j)+ Q( z) f =0 are discussed,where Q( z) is a transcendental entire function of finite order,and Pj( e- z) are non-constant polynomials. Some conditions on Q( z) are given which can guarantee that every non-rivial solution of the equation is infinite order,the growth of solutions to the corresponding non-homogeneous differential equation is discussed.

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What this paper is about

The growth of solutions of the higher order linear differential equations f( k)+ ∑j = 1Pj( e-z) f( j)+ Q( z) f =0 are discussed,where Q( z) is a transcendental entire function of finite order,and Pj( e- z) are non-constant polynomials. Some conditions on Q( z) are given which can guarantee that every non-rivial solution of the equation is infinite order,the growth of solutions to the corresponding non-homogeneous differential equation is discussed.

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Available abstract

The growth of solutions of the higher order linear differential equations f( k)+ ∑j = 1Pj( e-z) f( j)+ Q( z) f =0 are discussed,where Q( z) is a transcendental entire function of finite order,and Pj( e- z) are non-constant polynomials. Some conditions on Q( z) are given which can guarantee that every non-rivial solution of the equation is infinite order,the growth of solutions to the corresponding non-homogeneous differential equation is discussed.

Key concepts: Mathematics, Order (exchange), Transcendental number, Differential equation, Homogeneous differential equation, Entire function, Homogeneous, Constant (computer programming)

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