ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

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doi:10.1016/S0252-9602(18)30786-0

Abstract:

In this article, the existence of finite order entire solutions of nonlinear difference equations fⁿ + P_d(z, f)=p₁e^α₁z + p₂e^α₂z are studied, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d(≤ n-2), p₁, p₂ are small meromorphic functions of e^z, and α₁, α₂ are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions.

Key words: Nevanlinna theory, difference polynomial, difference equation, entire solution

Huifang LIU, Zhiqiang MAO. ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS[J].Acta mathematica scientia,Series B, 2018, 38(3): 819-828.

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