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<p>In this paper, we investigate the existence of solutions to an elliptic problem with natural growth term, diffuse measure data and Neumann boundary conditions. Using approximation methods via Yosida regularization and truncation, along with maximal monotone operator methods in Banach spaces, we prove the existence of a renormalized solution. We further describe how our notion of solution relates to the entropy solution framework.</p>

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Nonlinear Elliptic Problem Involving Natural Growth Term, Measure Data, Variable Exponent and Neumann Boundary Conditions

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Ibrahime Konaté,
  • Stanislas Ouaro

摘要

In this paper, we investigate the existence of solutions to an elliptic problem with natural growth term, diffuse measure data and Neumann boundary conditions. Using approximation methods via Yosida regularization and truncation, along with maximal monotone operator methods in Banach spaces, we prove the existence of a renormalized solution. We further describe how our notion of solution relates to the entropy solution framework.