Entire Solutions to a Certain Type of Differential-difference Equations [一类微分差分方程的整函数解]

作者：Wu L.H.; Zhang R.R.; Huang Z.B.^*

来源：Acta Mathematica Sinica (Chinese Series), 2021, 64(3): 471-478.

• Difference equation
• Differential-difference equation
• Entire solution

We investigate the nonlinear differential-difference equations of form f(z)n+ L(z, f)=q(z)ep(z), where n ≥ 2, L(z, f)(? 0) is a linear differential-difference polynomial in f(z), with small functions as its coefficients, p(z) and q(z) are non-vanishing polynomials. We first obtain that n=2 and f(z) satisfies λ(f)=σ(f)=deg p(z) if the equation possesses a transcendental entire solution of hyper order σ2(f)< 1. Furthermore, the exact form of the entire solutions of the equation is also obtained.

• 单位
  华南理工大学; 华南师范大学