## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Positive solutions of three-point boundary value problems for n-th order differential equations

#### Abstract

In this paper, we establish the existence and non-existence results of positive solutions for the (n-1,1) three-point boundary value problems consisting of the equation $$u^{(n)}+\lambda a(t)f(u(t))=0,\;\;\;t\in (0,1)$$ and one of the following boundary value conditions $$u(1)=\beta u(\eta ),\;\;u^{(i)}(0)=0\;\hbox{ for }\;i=1,2,\cdots,n-1$$ and $$u^{(n-1)}(1)=\beta u^{(n-1)}(\eta ),\;u^{(i)}(0)=0\;\hbox{ for }\;i=0,1,\cdot,n-2,$$ where $\eta \in [0,1)$, $\beta\in [0,1)$ and $a:\;(0,1)\rightarrow R$ may change sign. $f(0)>0$, $\lambda >0$ is a parameter. Our approach is based on the Leray-Schauder fixed point Theorem. This paper is motivated by Eloe and Henderson [6].

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 11, Number 2 (2004), 217-225.

Dates
First available in Project Euclid: 11 June 2004

https://projecteuclid.org/euclid.bbms/1086969313

Digital Object Identifier
doi:10.36045/bbms/1086969313

Mathematical Reviews number (MathSciNet)
MR2080423

Zentralblatt MATH identifier
1069.34015

#### Citation

Liu, Yuji; Ge, Weigao. Positive solutions of three-point boundary value problems for n-th order differential equations. Bull. Belg. Math. Soc. Simon Stevin 11 (2004), no. 2, 217--225. doi:10.36045/bbms/1086969313. https://projecteuclid.org/euclid.bbms/1086969313