We study existence and uniqueness of solutions of ($E_1$) $-\mathrm{\Delta }u+\frac{\mu }{|x{|}^2}u+g(u)=\nu$ in $\mathrm{\Omega }$, $u=\lambda$ on $\partial \mathrm{\Omega }$, where $\mathrm{\Omega }\subset {ℝ}_{+}^N$ is a bounded smooth domain such that $0\in \partial \mathrm{\Omega }$, $\mu \ge -\frac{N^2}{4}$ is a constant, $g$ a continuous nondecreasing function satisfying some integral growth condition and $\nu$ and $\lambda$ two Radon measures, respectively, in $\mathrm{\Omega }$ and on $\partial \mathrm{\Omega }$. We show that the situation differs considerably according the measure is concentrated at $0$ or not. When $g$ is a power we introduce a capacity framework which provides necessary and sufficient conditions for the solvability of problem ($E_1$).

中文翻译：

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具有 Leray-Hardy 势的半线性椭圆方程的边界奇点

我们研究 (${乙}_1$)$-\mathrm{\Delta }你+\frac{\mu }{|X{|}^2}你+G(你)=\nu$在$\mathrm{\Omega }$,$你=\lambda$上$\partial \mathrm{\Omega }$， 在哪里$\mathrm{\Omega }\subset {ℝ}_{+}^{ñ}$是一个有界平滑域，使得$0\in \partial \mathrm{\Omega }$,$\mu \ge -\frac{{ñ}^2}{4}$是一个常数，$G$满足某些积分增长条件的连续非减函数和$\nu$和$\lambda$两个氡测量，分别在$\mathrm{\Omega }$和上$\partial \mathrm{\Omega }$. 我们表明，由于措施集中在$0$或不。什么时候$G$是一种力量，我们引入了一个能力框架，为问题的可解决性提供了充分的必要条件（${乙}_1$）。