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<p>In this paper, we consider the existence of positive weak solutions for a class of quasilinear elliptic operators containing <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p(\cdot ) \)</EquationSource> </InlineEquation>-Laplacian and mean curvature operator with Robin boundary conditions. The results for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(p(\cdot )\)</EquationSource> </InlineEquation>-Laplacian are known, however, we attempt in this paper to extend the results for a class of quasilinear elliptic operators containing not only <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(p(\cdot )\)</EquationSource> </InlineEquation>-Laplacian but also the mean curvature operator.</p>

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Positive weak solutions of the Robin problem for a class of quasilinear elliptic equations containing the \(p(\cdot )\)-Laplacian and the mean curvature operator

  • 期刊论文

  • 发表日期：

    2025年11月13日

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  • Junichi Aramaki

摘要

In this paper, we consider the existence of positive weak solutions for a class of quasilinear elliptic operators containing \(p(\cdot ) \) -Laplacian and mean curvature operator with Robin boundary conditions. The results for \(p(\cdot )\) -Laplacian are known, however, we attempt in this paper to extend the results for a class of quasilinear elliptic operators containing not only \(p(\cdot )\) -Laplacian but also the mean curvature operator.