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2008 Multiplicity results for semipositone two-point boundary value problems
Andrew Arndt, Stephen Robinson
Involve 1(2): 123-133 (2008). 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 c0, 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.

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Andrew Arndt. Stephen Robinson. "Multiplicity results for semipositone two-point boundary value problems." Involve 1 (2) 123 - 133, 2008. https://doi.org/10.2140/involve.2008.1.123

Information

Received: 10 June 2007; Accepted: 6 December 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1156.34305
MathSciNet: MR2429653
Digital Object Identifier: 10.2140/involve.2008.1.123

Subjects:
Primary: 34B15

Keywords: boundary value problem , positone , semipositone , upper and lower solution

Rights: Copyright © 2008 Mathematical Sciences Publishers

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