ON EXISTENCE OF SOLUTIONS OF DIFFERENCE RICCATI EQUATION

Zongxuan CHEN; Kwang Ho SHON

doi:10.1007/s10473-019-0111-z

Acta mathematica scientia, Series B >

2019 , Vol. 39 >Issue 1: 139 - 147

DOI: https://doi.org/10.1007/s10473-019-0111-z

Articles

ON EXISTENCE OF SOLUTIONS OF DIFFERENCE RICCATI EQUATION

Zongxuan CHEN ,
Kwang Ho SHON

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1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
2. Department of Mathematics, College of Natural Sciences, Pusan National University, Busan, 609-735, Korea

Received date: 2017-09-11

Revised date: 2018-01-01

Online published: 2019-03-13

Supported by

The research was supported by the National Natural Science Foundation of China (11771090, 11761035, 11871260) and the Natural Science Foundation of Guangdong Province in China (2016A030310106, 2016A030313745).

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Abstract

Consider the difference Riccati equation f(z+1)=A(z)f(z)+B(z)/C(z)f(z)+D(z), where A, B, C, D are meromorphic functions, we give its solution family with one-parameter

where Q(z) is any constant in C or any periodic meromorphic function with period 1, and f₀(z), f₁(z), f₂(z) are its three distinct meromorphic solutions.

Key words： difference Riccati equation; solution family; order of growth

Cite this article

Zongxuan CHEN , Kwang Ho SHON . ON EXISTENCE OF SOLUTIONS OF DIFFERENCE RICCATI EQUATION[J]. Acta mathematica scientia, Series B, 2019 , 39(1) : 139 -147 . DOI: 10.1007/s10473-019-0111-z

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