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Abstract <p>The prime intention of this paper is to study the conditions for existence and the forms of entire solutions of the systems of nonlinear difference and second-order partial differential-difference Fermat-type equations in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8278_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{C}^{2}\)</EquationSource> <!--LobJMat2460691Biswas-m3--> </InlineEquation>. One of our main results extends a result of [<CitationRef CitationID="CR15">15</CitationRef>] and other results correspond to some new forms of equations that have never been tackled in the literature. We also illustrate a handful number of examples to show the accuracy of our results.</p>

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Entire Solutions for the Systems of Second-Order Partial Differential-Difference Fermat-Type Equations in \(\mathbb{C}^{2}\)

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Tania Biswas,
  • Sayantan Maity

摘要

Abstract

The prime intention of this paper is to study the conditions for existence and the forms of entire solutions of the systems of nonlinear difference and second-order partial differential-difference Fermat-type equations in \(\mathbb{C}^{2}\) . One of our main results extends a result of [15] and other results correspond to some new forms of equations that have never been tackled in the literature. We also illustrate a handful number of examples to show the accuracy of our results.