Vol. 1, No. 2, 2008

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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

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