We study singular radial solutions of the semilinear elliptic equation \(\Delta u + f(u) = 0\) on finite balls in \(\mathbf{R}^N\) with \(N \ge 3\). We assume that f satisfies either \(f(u) = u^p+o(u^p)\) with \(p > (N+2)/(N-2)\) or \(f(u) = e^u+ o(e^u)\) as \(u \rightarrow \infty \). We provide the existence and uniqueness of the singular radial solution, and show the convergence of regular radial solutions to the singular solution. Some applications to the bifurcation diagram of an elliptic Dirichlet problem are also given. Our results generalize and improve some known results in the literature.

我们研究\（\ mathbf {R} ^ N \）中带有\（N \ ge 3 \）的有限球上半线性椭圆方程\（\ Delta u + f（u）= 0 \）的奇异径向解。我们假设f满足\（f（u）= u ^ p + o（u ^ p）\）和\（p>（N + 2）/（N-2）\）或\（f（u） = e ^ u + o（e ^ u）\）为\（u \ rightarrow \ infty \）。我们提供奇异径向解的存在性和唯一性，并展示正则径向解对奇异解的收敛性。还给出了椭圆Dirichlet问题的分叉图的一些应用。我们的结果概括并改进了文献中的一些已知结果。