On admissible entire solutions of Pell type functional equation f2 + ag2 = 1
Journal of Mathematical Analysis and Applications(2019)
摘要
Given a non-zero entire function a, we would like to find entire functions f and g such that a is a small function of f and g and the pair (f,g) satisfies the Pell type functional equation: f2+ag2=1. Such pair (f,g) is called an admissible entire solution and is studied for the first time in this note. We will show that all admissible solutions must be of certain form and they always exist. This will allow us to obtain some results on entire solutions of the related non-linear differential equation f2+a(f(k))2=1 where k is a positive integer.
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关键词
Pell type functional equations,Entire admissible solutions,Non-linear differential equation
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