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We study the existence of weak solutions to nonlinear elliptic inclusions with singularities: \( \zeta (u) + A(u) + H(x,u,\nabla u) \ni \frac{f}{u^\gamma }, \) where \( A \) is a Leray–Lions operator, \( \zeta \) is maximal monotone graph with \( 0 \in \zeta (0) \) , the nonlinear term \( H \) has natural growth of order \(p\) but satisfies a sign condition, and \( f \in L^\infty (\Omega ) \) , \( \gamma > 0 \) .

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Analysis of Strongly Nonlinear Elliptic Equations with Singular Data and Natural Growth Terms

  • 会议论文

  • 发表日期：

    2026年

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  • Mohamed Bahadi,
  • Morad Ouboufettal,
  • Youssef Akdim

摘要

We study the existence of weak solutions to nonlinear elliptic inclusions with singularities: \( \zeta (u) + A(u) + H(x,u,\nabla u) \ni \frac{f}{u^\gamma }, \) where \( A \) is a Leray–Lions operator, \( \zeta \) is maximal monotone graph with \( 0 \in \zeta (0) \) , the nonlinear term \( H \) has natural growth of order \(p\) but satisfies a sign condition, and \( f \in L^\infty (\Omega ) \) , \( \gamma > 0 \) .