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<p>The main objective of this article is to explore the existence and characterization of transcendental solutions to various Fermat-type functional equations with polynomial coefficients in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathbb {C}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. By utilizing the Nevanlinna theory of meromorphic functions in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\mathbb {C}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> as a fundamental tool in our examination. We investigate the existence and forms of transcendental solutions to quadratic trinomial equations in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({\mathbb {C}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. The main results of this article improve several existing findings. Furthermore, we provide relevant examples to validate each result and include several remarks to support our improvements.</p>

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Characterization of Transcendental Solutions of Differential-Difference Equations in \({\mathbb {C}}^n\)

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Molla Basir Ahamed,
  • Sanju Mandal

摘要

The main objective of this article is to explore the existence and characterization of transcendental solutions to various Fermat-type functional equations with polynomial coefficients in \({\mathbb {C}}^n\) C n . By utilizing the Nevanlinna theory of meromorphic functions in \({\mathbb {C}}^n\) C n as a fundamental tool in our examination. We investigate the existence and forms of transcendental solutions to quadratic trinomial equations in \({\mathbb {C}}^n\) C n . The main results of this article improve several existing findings. Furthermore, we provide relevant examples to validate each result and include several remarks to support our improvements.