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
DOI: 10.2140/involve.2008.1.123
Abstract

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

u′′ + f(u) = 0, in (0,1),u(0) = u(1) = 0,

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 2000
Primary: 34B15
Milestones
Received: 10 June 2007
Accepted: 6 December 2007
Published: 1 July 2008

Communicated by John V. Baxley
Authors
Andrew Arndt
Department of Mathematics
Wake Forest University
Winston–Salem, NC 27109
United States
Stephen B. Robinson
Department of Mathematics
Wake Forest University
Winston–Salem, NC 27109
United States