Scholarlink

<p>In this paper, we consider a special class of fourth-order Leray–Lions operator with Hardy potential. Using a local minimum theorem and its variants of Bonanno–Candito (Adv Nonlinear Stud 14(4):915–939, 2014) and the critical theorem of Bonanno–Marano (Nonlinear Anal 89(1):1–10, 2010), we consider the existence of at least one non-trivial weak solution and three weak solutions, respectively. In addition, an example is given to support our theoretical analysis. To the best of our knowledge, this paper represents one of the initial contributions to the investigation of Leray–Lions operators exhibiting non-standard growth and Hardy potentials, where the source term can be singular and change sign on the domain <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41808_2025_336_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\( \Omega ,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> introducing additional difficulties and complexities in the analysis.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Analysis and applications of a nonlinear coupled system with a fourth-order Leray–Lions operator involving Hardy potential

  • 期刊论文

  • 发表日期：

    2025年4月30日

查看全文
  • Khaled Kefi,
  • Guoping Yang,
  • Mohamed Karim Hamdani,
  • Jian Liu

摘要

In this paper, we consider a special class of fourth-order Leray–Lions operator with Hardy potential. Using a local minimum theorem and its variants of Bonanno–Candito (Adv Nonlinear Stud 14(4):915–939, 2014) and the critical theorem of Bonanno–Marano (Nonlinear Anal 89(1):1–10, 2010), we consider the existence of at least one non-trivial weak solution and three weak solutions, respectively. In addition, an example is given to support our theoretical analysis. To the best of our knowledge, this paper represents one of the initial contributions to the investigation of Leray–Lions operators exhibiting non-standard growth and Hardy potentials, where the source term can be singular and change sign on the domain \( \Omega ,\) Ω , introducing additional difficulties and complexities in the analysis.