On a nonlinear Robin problem with an absorption term on the boundary and L 1 data

Abstract

We deal with existence and uniqueness of nonnegative solutions to: − Δ u = f ( x ) , in Ω , ∂ u ∂ ν + λ ( x ) u = g ( x ) u η , on ∂ Ω , \left\{\begin{array}{ll}-\Delta u=f\left(x),\hspace{1.0em}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ \frac{\partial u}{\partial \nu }+\lambda \left(x)u=\frac{g\left(x)}{{u}^{\eta }},\hspace{1.0em}& \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}\partial \Omega ,\end{array}\right. where η ≥ 0 \eta \ge 0 and f , λ f,\lambda , and g g are the nonnegative integrable functions. The set Ω ⊂ R N ( N > 2 ) \Omega \subset {{\mathbb{R}}}^{N}\left(N\gt 2) is open and bounded with smooth boundary, and ν \nu

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关于边界上有吸收项和 L 1 数据的非线性罗宾问题

其中 η ≥ 0 \eta \ge 0，f , λ f,\lambda , 和 g g 是非负可积分函数。集合 Ω ⊂ R N ( N > 2 ) \子集{{\mathbb{R}}}^{N}left(N\gt 2) 是开放且有界的，边界光滑，且 ν \nu </jat

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