Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 112, pp. 1-7.
Title: Multiple positive solutions for nonlinear third-order
three-point boundary-value problems
Authors: Li-Jun Guo (Lanzhou Univ. of Technology, China)
Jian-Ping Sun (Lanzhou Univ. of Technology, China)
Ya-Hong Zhao (Lanzhou Univ. of Technology, China)
Abstract:
This paper concerns the nonlinear third-order three-point
boundary-value problem
$$\displaylines{
u'''(t)+h(t)f(u(t))=0, \quad t\in (0,1), \cr
u(0)=u'(0)=0, \quad u'(1)=\alpha u'(\eta ),
}$$
where $0<\eta <1$ and $1<\alpha <\frac 1\eta $. First,
we establish the existence of at least three positive
solutions by using the well-known Leggett-Williams fixed point theorem.
And then, we prove the existence of at least $2m-1$ positive
solutions for arbitrary positive integer $m$.
Submitted April 18, 2007. Published August 18, 2007.
Math Subject Classifications: 34B10, 34B18.
Key Words: Third-order boundary value problem; positive solution;
three-point boundary value problem; existence; cone; fixed point.