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Abstract <p>In this paper, we discuss the existence of meromorphic solutions to the following system of difference equations</p> <p><Equation ID="Equa"> <EquationSource Format="TEX">\(\begin{cases}f(z+c)=e^{P}f-ae^{P}+a,\\ f(z+c)=e^{Q}f-be^{Q}+b,\end{cases}\)</EquationSource> <!--ContMath2460227Fu-m1--> </Equation></p> <p>where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P\)</EquationSource> <!--ContMath2460227Fu-m2--> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Q\)</EquationSource> <!--ContMath2460227Fu-m3--> </InlineEquation> are entire functions, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(a\)</EquationSource> <!--ContMath2460227Fu-m4--> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(b\)</EquationSource> <!--ContMath2460227Fu-m5--> </InlineEquation> are distinct complex numbers. Additionally, this work elucidates the application of these findings, thereby enhancing uniqueness results associated with meromorphic functions <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(f(z)\)</EquationSource> <!--ContMath2460227Fu-m6--> </InlineEquation> and their shifts <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(f(z+c)\)</EquationSource> <!--ContMath2460227Fu-m7--> </InlineEquation>.</p>

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Solutions to a Class of Difference Equations Systems and Their Applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月18日

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  • Y. Fu,
  • X. Qi

摘要

Abstract

In this paper, we discuss the existence of meromorphic solutions to the following system of difference equations

\(\begin{cases}f(z+c)=e^{P}f-ae^{P}+a,\\ f(z+c)=e^{Q}f-be^{Q}+b,\end{cases}\)

where \(P\) and \(Q\) are entire functions, \(a\) and \(b\) are distinct complex numbers. Additionally, this work elucidates the application of these findings, thereby enhancing uniqueness results associated with meromorphic functions \(f(z)\) and their shifts \(f(z+c)\) .