一类二阶非局部边值问题的正解

Positive solutions of second order nonlocal boundary value problem

讨论一类奇异二阶常微分方程非局部边值问题,利用锥上的不动点指数定理,通过分析非线性项f和g在零点和无穷远点的增长性以及与参数λ之间的关系,建立问题正解的存在性、不存在性与多解性结果,并给出研究这一问题正解的关键条件g M+h M<1.

The paper is concerned with a nonlocal boundary value problem of second-order singular ordinary dif- ferential equation. Applying the fixed-point index theorem in cones, we show the relationships between the growth off and g （ at zero and infinity） and the Parameter A, such that the problem has no, one and multiple positive（s）. Also, a key condition of discussing the existence of positive solution（s） for the nonloeal boundary value problem is put forward,which is stated as： gM ＋ hM 〈 1 .