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<p>Under the assumption of finite energy, positive solutions to the critical p-Laplace equation in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3141_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3141_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt; p&lt;n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation> have been classified completely by moving plane method. In this paper, the author provide a new approach to obtain the classification results for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3141_Article_IEq3.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="91" /> </InlineMediaObject> <EquationSource Format="TEX">\(\frac{n+1}{3}&lt; p&lt;n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfrac> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>3</mn> </mfrac> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation>, without any further assumptions.</p>

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On the classification of entire solutions to the critical p-Laplace equation

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Qianzhong Ou

摘要

Under the assumption of finite energy, positive solutions to the critical p-Laplace equation in \({\mathbb {R}}^n\) R n for \(1< p<n\) 1 < p < n have been classified completely by moving plane method. In this paper, the author provide a new approach to obtain the classification results for \(\frac{n+1}{3}< p<n\) n + 1 3 < p < n , without any further assumptions.