Multiplicity results for semipositone two-point boundary value problems

where the function $f$ resembles $f (u) = λ (exp (a u ∕ (a + u)) - c)$ for some constants $c \geq 0$ , $λ > 0$ , $a > 4$ . 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

Vol. 1, No. 2, 2008

Andrew Arndt and Stephen B. Robinson

Abstract

Keywords

Mathematical Subject Classification 2000

Milestones

Authors