Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 23, pp. 1-10.
Title: Multiple positive solutions for fourth-order three-point
p-Laplacian boundary-value problems
Authors: Hanying Feng (Beijing Inst. of Technology, China)
Meiqiang Feng (Beijing Inst. of Technology, China)
Ming Jiang (Shijiazhuang Mechanical Engineering College, China)
Weigao Ge (Beijing Inst. of Technology, China)
Abstract:
In this paper, we study the three-point boundary-value problem
for a fourth-order one-dimensional $p$-Laplacian differential
equation
$$
\big(\phi_p(u''(t))\big)''+ a(t)f\big(u(t)\big)=0,
\quad t\in (0,1),
$$
subject to the nonlinear boundary conditions:
$$\displaylines{
u(0)=\xi u(1),\quad u'(1)=\eta u'(0),\cr
(\phi _{p}(u''(0))' =\alpha _{1}(\phi _{p}(u''(\delta))',
\quad u''(1)=\sqrt[p-1]{\beta _{1}}u''(\delta),
}$$
where $\phi_{p}(s)=|s|^{p-2}s$, $p>1$. Using the five functional
fixed point theorem due to Avery, we obtain sufficient conditions
for the existence of at least three positive solutions.
Submitted November 30, 2006. Published February 4, 2007.
Math Subject Classifications: 34B10, 34B15, 34B18.
Key Words: Fourth-order boundary-value problem; one-dimensional p-Laplacian;
five functional fixed point theorem; positive solution