Some results on transcendental entire solutions of certain nonlinear differential-difference equations

2021/02/04 by Nan Li, Li, Nan, Jiachuan Geng +3
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Primary 30D35 #Secondary 39B32 #math.CV #msc:30D35 #msc:39B32

paper · pdf · doi:10.48550/arxiv.2102.02508

arxiv created 2021/02/04 · arxiv updated 2021/02/05

Abstract

In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms: f²(z)+\widetildeω f(z)f'(z)+q(z)e^Q(z)f(z+c)=u(z)e^v(z), and fⁿ(z)+ωf^n-1(z)f'(z)+q(z)e^Q(z)f(z+c)=p₁e^λ₁ z+p₂e^λ₂ z, n≥ 3, where ω is a constant, \widetildeω, c, λ₁, λ₂, p₁, p₂ are non-zero constants, q, Q, u, v are polynomials such that Q,v are not constants and q,u\not≡0. Our results are improvements and complements of some previous results.

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