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Meromorphic solutions of fn+Pd(f)=p1eα1z+p2eα2z+p3eα3z
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Journal Article
Meromorphic solutions of fn+Pd(f)=p1eα1z+p2eα2z+p3eα3z
2022
Overview
By using Nevanlinna of the value distribution of meromorphic functions, we investigate the transcendental meromorphic solutions of the non-linear differential equationfn+Pd(f)=p1eα1z+p2eα2z+p3eα3z,where Pd(f) is a differential polynomial in f of degree d(0≤d≤n−3) with small meromorphic coefficients and pi,αi(i=1,2,3) are nonzero constants. We show that the solutions of this type equation are exponential sums and they are in Γ0∪Γ1∪Γ3 which will be given in Section 1. Moreover, we give some examples to illustrate our results.
Publisher
American Institute of Mathematical Sciences
Subject
