In this paper,some multiple positive solu tions theorems of a class of operator equation are established by using fixed po int index and the spectral radius of the relative linear operator.Multiple posit ive solutions of some singular boundary value problems are obtained by using the above-mentioned results for operators.%利用不动点指数理论对一类算子方程建立了多重正 解的存在性定理,通过相应的线性算子的谱半径,给出其正解存在与具有多解的条件。用得 到的结果给出了一类奇异半线性微分方程边值问题解的存在性,改进和推广了文献[1~4] 的工作。
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