Existence of positive solutions for semipositone multi-point boundary value problems

In this paper, the existence of positive solutions for a semipositone second-order multi-point boundary value problem is investigated. By using Krasnosel’skii’s fixed point theorem, sufficient conditions that guarantee the existence of at least one positive solution are obtained.

► A second-order multipoint boundary value problem is investigated.
► The existence of positive solutions is obtained under the condition that nonlinearity ff is semi-positone.
► The results of existence contain not only for positive parameter λλ sufficiently small but also λλ sufficiently large.