#### Vol. 1, No. 2, 2008

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Multiplicity results for semipositone two-point boundary value problems

### Andrew Arndt and Stephen B. Robinson

Vol. 1 (2008), No. 2, 123–133
##### Abstract

In this paper we address two-point boundary value problems of the form

where the function $f$ resembles $f\left(u\right)=\lambda \left(exp\left(au∕\left(a+u\right)\right)-c\right)$ for some constants $c\ge 0$, $\lambda >0$, $a>4$. We prove the existence of positive solutions for the semipositone case where $f\left(0\right)<0$, and further prove multiplicity under certain conditions. In particular we extend theorems from Henderson and Thompson to the semipositone case.

##### Keywords
positone, semipositone, boundary value problem, upper and lower solution
Primary: 34B15