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<p>This paper investigates a class of anisotropic quasilinear elliptic equations involving convection terms and unbounded coefficients in a bounded domain. The problem is studied within the framework of anisotropic Sobolev spaces and the sub-supersolution method. Under suitable growth conditions on the nonlinear convection term, we establish the existence of weak solutions lying between a given subsolution and supersolution. Moreover, we prove that the set of all weak solutions is uniformly bounded. Our approach relies on truncation techniques, Moser’s iteration, and the theory of pseudomonotone operators.</p>

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Existence and boundedness of solutions for anisotropic quasilinear elliptic equations with convection and unbounded coefficients

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月28日

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  • Abdolrahman Razani,
  • Sami Baraket

摘要

This paper investigates a class of anisotropic quasilinear elliptic equations involving convection terms and unbounded coefficients in a bounded domain. The problem is studied within the framework of anisotropic Sobolev spaces and the sub-supersolution method. Under suitable growth conditions on the nonlinear convection term, we establish the existence of weak solutions lying between a given subsolution and supersolution. Moreover, we prove that the set of all weak solutions is uniformly bounded. Our approach relies on truncation techniques, Moser’s iteration, and the theory of pseudomonotone operators.