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Abstract <p>The aim of this paper is to investigate the conditions for the existence and structure of entire solutions to systems of nonlinear second-order partial differential-difference equations of Fermat type in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb{C}^{2}\)</EquationSource> <!--LobJMat2561265Biswas-m1--> </InlineEquation>. One of our main results extends two theorems from [<CitationRef CitationID="CR26">26</CitationRef>] to the setting of systems of equations, while other findings concern novel forms of equations that, to the best of our knowledge, have not been explored in the existing literature. Several illustrative examples are provided to support our main results.</p>

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Entire Solutions for the Systems of Second-Order Partial Differential-Difference Fermat-Type Equations in Several Complex Variables

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Tania Biswas,
  • Sayantan Maity

摘要

Abstract

The aim of this paper is to investigate the conditions for the existence and structure of entire solutions to systems of nonlinear second-order partial differential-difference equations of Fermat type in \(\mathbb{C}^{2}\) . One of our main results extends two theorems from [26] to the setting of systems of equations, while other findings concern novel forms of equations that, to the best of our knowledge, have not been explored in the existing literature. Several illustrative examples are provided to support our main results.