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<p>In this paper, we study the existence of positive solutions for a nonlocal singular elliptic coupled system involving <i>N</i>-Laplace operator. The source term of the system is expressed as the sum of two components: one with subcritical, critical, or supercritical exponential growth controlled by the Trudinger–Moser inequality, and the other being singular at the origin. We also investigate the asymptotic behavior of the solutions with respect to the parameters. Furthermore, we prove that no solutions exist for our system in dimension <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2006_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">$N=2$</EquationSource> </InlineEquation>.</p>

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A nonlocal coupled system involving N-Laplacian operator: existence and asymptotic behavior of positive solutions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月27日

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  • Rafik Guefaifia,
  • Chahinez Bellamouchi,
  • Salah Boulaaras,
  • Rashid Jan

摘要

In this paper, we study the existence of positive solutions for a nonlocal singular elliptic coupled system involving N-Laplace operator. The source term of the system is expressed as the sum of two components: one with subcritical, critical, or supercritical exponential growth controlled by the Trudinger–Moser inequality, and the other being singular at the origin. We also investigate the asymptotic behavior of the solutions with respect to the parameters. Furthermore, we prove that no solutions exist for our system in dimension N = 2 $N=2$ .