In this paper, we are concerned with the radial solutions for the eigenvalue problem of a singular $k$-Hessian equation. By constructing the upper and lower solutions of the $k$-Hessian equation, the existence of a radial solution for the eigenvalue problem is established via Schauder’s fixed point theorem under the case where the nonlinearity possesses a singularity with respect to the space variable.

中文翻译：

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奇异k-Hessian方程的特征值问题

在本文中，我们关注奇异的特征值问题的径向解 $克$- 黑森方程。通过构造上、下解$克$-Hessian方程，在非线性相对于空间变量具有奇异性的情况下，通过Schauder不动点定理建立了特征值问题径向解的存在性。