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<p>Working in the framework of variable exponent Lebesgue–Sobolev spaces, we prove the existence of solutions to a nonhomogeneous quasilinear elliptic equation with convection term subject to Dirichlet boundary condition. Since the nonlinearity considered depends on the gradient of the unknown function, variational methods cannot be applied. Our approach relies on the Leray–Schauder principle.</p>

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Existence of solutions to a nonhomogeneous quasilinear elliptic equation with convection and Dirichlet boundary condition

  • 期刊论文

  • 发表日期：

    2025年4月18日

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  • Sidi Hamidou Jah,
  • Lotfi Riahi

摘要

Working in the framework of variable exponent Lebesgue–Sobolev spaces, we prove the existence of solutions to a nonhomogeneous quasilinear elliptic equation with convection term subject to Dirichlet boundary condition. Since the nonlinearity considered depends on the gradient of the unknown function, variational methods cannot be applied. Our approach relies on the Leray–Schauder principle.