Abstract

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

where the function f resembles f(u) = λ(exp(au ∕ (a + u)) − c) for some constants c ≥ 0, λ > 0, a > 4. We prove the existence of positive solutions for the semipositone case where f(0) < 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

Mathematical Subject Classification

Primary: 34B15

Authors