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<p>We have studied the existence of solutions for a class of elliptic boundary value problems with p-Laplacian under the Dirichlet boundary condition. The main novelties include the dependence of the reaction term on the gradient of the solution and the inclusion of the Leray-Lions operator in the differential part. The compactness of the solution set is also proved. We used sub-supersolution method to obtain the existence of solutions.</p>

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A class of nonlinear elliptic equations with dependence on the gradient

  • 期刊论文

  • 发表日期：

    2025年6月19日

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  • Rupali Kumari,
  • Rasmita Kar

摘要

We have studied the existence of solutions for a class of elliptic boundary value problems with p-Laplacian under the Dirichlet boundary condition. The main novelties include the dependence of the reaction term on the gradient of the solution and the inclusion of the Leray-Lions operator in the differential part. The compactness of the solution set is also proved. We used sub-supersolution method to obtain the existence of solutions.