一类奇异二阶常微分方程三点边值问题的多个正解

Multiple positive solutions to singular boundary value problems of a class of second order three-point

讨论一类奇异非线性二阶常微分方程三点边值问题正解的存在性问题,首先得出与所研究奇异边值问题等价的积分算子方程,其次是在C[0,1]空间上构造锥并且证明算子在所构造的锥上是全连续算子,最后运用锥拉伸和压缩不动点定理,在次线性条件下,解决了这类奇异非线性二阶常微分方程三点边值问题正解的存在性问题,并获得了该类问题至少存在两个C[0,1]正解的充分条件.

In order to discuss the existence of positive solutions to singular boundary vet problems of a class of second order three-point sublinear differential equations, the paper proceeds the research to .solve this type of problem by firstly constructing the integral equation of being equivalent to the problem, secondly constructing a cone and prollfing the integral equation being completely continuous in the cone, and finally solving the problem with fixed point principle on cone. A sufficient condition for the existence of C[0,1] multiple positive solutions is given to singular boundary value problems of a class of second order three-point sublinear differential equations.