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Abstract <p>This article investigates the existence and explicit forms of solutions of a quadratic trinomial partial differential difference equation and a system of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(k\)</EquationSource> <!--ContMath2670003Haldar-m3--> </InlineEquation>th order partial differential difference equations in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb{C}^{2}\)</EquationSource> <!--ContMath2670003Haldar-m4--> </InlineEquation>. One main result extends a recent finding in the literature, while the other offers a novel contribution. We include several illustrative examples to demonstrate the accuracy and applicability of the results.</p>

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On Entire Solutions of Quadratic Trinomial Partial Differential Difference Equations in\(\boldsymbol{\mathbb{C}^{2}}\)

  • 期刊论文

  • 发表日期：

    2026年6月20日

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  • G. Haldar,
  • D. C. Pramanik,
  • A. Roy

摘要

Abstract

This article investigates the existence and explicit forms of solutions of a quadratic trinomial partial differential difference equation and a system of \(k\) th order partial differential difference equations in \(\mathbb{C}^{2}\) . One main result extends a recent finding in the literature, while the other offers a novel contribution. We include several illustrative examples to demonstrate the accuracy and applicability of the results.