中文摘要：

考虑了一类奇异（k，n-k）共轭边值问题，利用锥上的不动点理论与不动点指数理论获得了存在一个正解和多个正解的充分条件．

英文摘要：

A class of singular （k,n--k） conjuate bundary value problems is studied. The sufficient conditions for existence of one positive solution and multiple positive solutions are given by using of the fixed point theorem and the fixed point index theorem on cone.