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<p>In this paper, we prove the existence of least energy nodal solutions to a mixed local-nonlocal <i>p</i>-Laplacian operator problem involving singularities. We employ the Nehari manifold approach, constrained variational method, and Brouwer degree theory to establish our result. The obtained results are also new and novel even for the case <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p=2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Least energy nodal solutions for mixed local-nonlocal equations involving singularity

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Souvik Bhowmick,
  • Sekhar Ghosh,
  • Kamel Saoudi

摘要

In this paper, we prove the existence of least energy nodal solutions to a mixed local-nonlocal p-Laplacian operator problem involving singularities. We employ the Nehari manifold approach, constrained variational method, and Brouwer degree theory to establish our result. The obtained results are also new and novel even for the case \(p=2\) p = 2 .