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<p>This paper is devoted to studying the possible forms of entire solutions of some differential-difference equations, which originate from the Fermat type functional equation. Our theorems generalize and supplement the results given by Wang et al. (Bull. Malays. Math. Sci. Soc.&#xa0;43:2951-2965, 2020), in which they only discussed the entire solutions of finite order to the similar differential-difference equations with the term <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40315_2025_588_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(e^{\alpha z+\beta }\)</EquationSource> </InlineEquation> where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40315_2025_588_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha ,\beta\)</EquationSource> </InlineEquation> are constants. We replace <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40315_2025_588_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha z+\beta\)</EquationSource> </InlineEquation> by a non-constant polynomial, and consider the entire solutions under the weakened growth condition.</p>

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On Entire Solutions of Two Types of Differential-Difference Equations

  • 期刊论文

  • 发表日期：

    2025年7月2日

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  • Xinyang Liu,
  • Feng Lü,
  • Weiran Lü,
  • Jun Wang

摘要

This paper is devoted to studying the possible forms of entire solutions of some differential-difference equations, which originate from the Fermat type functional equation. Our theorems generalize and supplement the results given by Wang et al. (Bull. Malays. Math. Sci. Soc. 43:2951-2965, 2020), in which they only discussed the entire solutions of finite order to the similar differential-difference equations with the term \(e^{\alpha z+\beta }\) where \(\alpha ,\beta\) are constants. We replace \(\alpha z+\beta\) by a non-constant polynomial, and consider the entire solutions under the weakened growth condition.