Some results for a certain class of nonlinear binomial differential equation

Qiyuan Feng; Junfeng Xu; Qiyuan Feng; Junfeng Xu

doi:10.3934/math.2026292

AIMS Mathematics

2026, Volume 11, Issue 3: 7098-7114. doi: 10.3934/math.2026292

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Research article

Some results for a certain class of nonlinear binomial differential equation

Qiyuan Feng ,
Junfeng Xu ^,

School of Mathematics and Computational Sciences, Wuyi University, Jiangmen, Guangdong 529000, China

Received: 11 December 2025 Revised: 25 February 2026 Accepted: 11 March 2026 Published: 18 March 2026
MSC : 30D05, 30D35

In this paper, we study one class of nonlinear binomial differential equation
$ (f(z))^{n}+a(f^{(k)}(z))^{n} = p_{1}e^{\lambda_{1}z}+p_{2}e^{\lambda_{2}z}, $
where $ n, k\in \mathbb{N^{+}} $, $ a $, $ p_i $, and $ \lambda_i $ are nonzero constants for $ i = 1, 2 $. Some results answer the previous conjecture given by Linkui Gao and Junyang Gao.
- binomial differential equation,
- exponential polynomial,
- entire function,
- Wiman–Valiron theorem
Citation: Qiyuan Feng, Junfeng Xu. Some results for a certain class of nonlinear binomial differential equation[J]. AIMS Mathematics, 2026, 11(3): 7098-7114. doi: 10.3934/math.2026292

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Abstract

In this paper, we study one class of nonlinear binomial differential equation

$ (f(z))^{n}+a(f^{(k)}(z))^{n} = p_{1}e^{\lambda_{1}z}+p_{2}e^{\lambda_{2}z}, $

where $ n, k\in \mathbb{N^{+}} $, $ a $, $ p_i $, and $ \lambda_i $ are nonzero constants for $ i = 1, 2 $. Some results answer the previous conjecture given by Linkui Gao and Junyang Gao.

References

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