在不要求正规锥的条件下,利用A-proper半线性算子的不动点指数性质,本文给出了半线性方程正解的存在性结果.作为应用,我们获得了二阶m点共振边值问题正解的存在性.
Existence results of positive solutions for semilinear operator equations without the assumption of normal cones are obtained by the help of the properties of a fixed point index for A-proper semilinear operators in this paper.As an application of our results,we prove the existence theorem concerning the existence of positive solutions for the second order m-point boundary value problems at resonance.