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<p>In this paper, we obtain the existence of at least two nontrivial solutions for a Dirichlet-type differential inclusion problem involving the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((p_1(x),p_2(x))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplacian operator. Our approach is variational, and it is based on the nonsmooth critical point theory of locally Lipchitz functions.</p>

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Two solutions for a Dirichlet-type differential inclusion problem involving the \((p_1(x),p_2(x))\)-Laplacian operator

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Omar Darhouche,
  • Fouad Kissi,
  • Abdelaziz El hachmi

摘要

In this paper, we obtain the existence of at least two nontrivial solutions for a Dirichlet-type differential inclusion problem involving the \((p_1(x),p_2(x))\) ( p 1 ( x ) , p 2 ( x ) ) -Laplacian operator. Our approach is variational, and it is based on the nonsmooth critical point theory of locally Lipchitz functions.