On Entire Solutions of Nonlinear Differential-difference Equations

Da Zhuan QIN, Jian Ren LONG

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 435-446.

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PDF(425 KB)
Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 435-446. DOI: 10.12386/A2022sxxb0035

On Entire Solutions of Nonlinear Differential-difference Equations

  • Da Zhuan QIN, Jian Ren LONG
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Abstract

We consider the growth of solutions of differential-difference equation
fn(z)+q(z)eQ(z)f(k)(z+c)=p1eα1z+p2eα2z
and
fn(z)+q(z)eQ(z)Δcf=p1eλz+p2eλz,
where n1 and k1 are two integers, q(z) is a non-zero polynomial and Q(z) is a non-constant polynomial. c,λ,α1,α2,p1 and p2 are non-zero constants, α1α2. In particular, we show that exponential polynomial solutions satisfying certain conditions must reduce to rather specific forms, which is an improvement of previous results.

Key words

exponential polynomials / entire solutions / nonlinear differential-difference equations / finite order

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Da Zhuan QIN, Jian Ren LONG. On Entire Solutions of Nonlinear Differential-difference Equations. Acta Mathematica Sinica, Chinese Series, 2022, 65(3): 435-446 https://doi.org/10.12386/A2022sxxb0035

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