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In this paper, we study existence and properties of positive solutions for some elliptic systems like \( \left\{ \begin{array}{ll} u \in W_0^{1,2}(\Omega ): -\mathop {\textrm{div}}(B(x)\nabla u) + u = M(x)\nabla \psi \cdot \nabla u + f(x)\,, \\ \psi \in W_0^{1,2}(\Omega ): -\mathop {\textrm{div}}(M(x)\nabla \psi ) = u^{\theta }\,, \end{array} \right. \) where \(\Omega \) is a bounded open subset of \(\mathbb {R}^{N}\) , \(N > 2\) , \(f(x) \ge 0\) is a function in \(L^{\frac{N}{2}}(\Omega )\) , and \(0 < \theta < 1\) .

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Sublinear Elliptic Systems with a Drift Term

  • 会议论文

  • 发表日期：

    2025年

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  • Lucio Boccardo,
  • Luigi Orsina

摘要

In this paper, we study existence and properties of positive solutions for some elliptic systems like \( \left\{ \begin{array}{ll} u \in W_0^{1,2}(\Omega ): -\mathop {\textrm{div}}(B(x)\nabla u) + u = M(x)\nabla \psi \cdot \nabla u + f(x)\,, \\ \psi \in W_0^{1,2}(\Omega ): -\mathop {\textrm{div}}(M(x)\nabla \psi ) = u^{\theta }\,, \end{array} \right. \) where \(\Omega \) is a bounded open subset of \(\mathbb {R}^{N}\) , \(N > 2\) , \(f(x) \ge 0\) is a function in \(L^{\frac{N}{2}}(\Omega )\) , and \(0 < \theta < 1\) .