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Entire Solutions of a Certain Type of Nonlinear Differential-Difference Equations

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Abstract

The aim of the paper is to investigate all transcendental entire solutions of the following general nonlinear equation of the form \(f^{n}+P_{d}(z,f)=p_{1}e^{\alpha _{1}z}+p_{2}e^{\alpha _{2}z}\), where Pd(z,f) is a differential-difference polynomial in f of degree d. Our result is a generalization and complement of known results obtained by Liu-Mao, L\({\ddot {\mathrm {u}}}\) et al. and the references therein.

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Acknowledgements

The authors would like to thank the referees for their thorough comments and helpful suggestions.

Funding

Research supported by the Natural Science Foundation of Fujian Province, China (Grants Nos. 2018J01658, 2021J01651).

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Authors and Affiliations

  1. School of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of China

    Wen-Jie Hao

  2. School of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, People’s Republic of China

    Wen-Jie Hao & Jun-Fan Chen

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  1. Wen-Jie Hao
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  2. Jun-Fan Chen
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Correspondence to Jun-Fan Chen.

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Hao, WJ., Chen, JF. Entire Solutions of a Certain Type of Nonlinear Differential-Difference Equations. Acta Math Vietnam 47, 731–741 (2022). https://doi.org/10.1007/s40306-021-00464-9

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  • DOI: https://doi.org/10.1007/s40306-021-00464-9

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