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<p>Two purposes will be shown in this paper. The first one is to extend the classic Tumura–Clunie type theorem for meromorphic functions of one complex variable to meromorphic functions of several complex variables by using Clunie lemma. The second one is to characterize entire solutions of certain partial differential equations in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1756_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {C}}^{m}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>m</mi> </msup> </math></EquationSource> </InlineEquation>. Our results are extensions and generalizations of the previous theorems by Liao-Ye (J Aust Math Soc. 97:391–403, 2014) and Li (Am Math Soc 357:3169–3177, 2005).</p>

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Clunie lemma in several complex variables and application in PDEs

  • 期刊论文

  • 发表日期：

    2025年7月7日

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  • Wenjie Hao,
  • Qingcai Zhang

摘要

Two purposes will be shown in this paper. The first one is to extend the classic Tumura–Clunie type theorem for meromorphic functions of one complex variable to meromorphic functions of several complex variables by using Clunie lemma. The second one is to characterize entire solutions of certain partial differential equations in \({\mathbb {C}}^{m}\) C m . Our results are extensions and generalizations of the previous theorems by Liao-Ye (J Aust Math Soc. 97:391–403, 2014) and Li (Am Math Soc 357:3169–3177, 2005).