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.

• 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。