Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 83, pp. 1-10.
Title: Positive solutions for a nonlinear n-th order
m-point boundary-value problem
Authors: Jiehua Zhang (Fuzhou Univ., Fuzhou, China)
Yanping Guo (Hebei Univ. of Science and Tech., China)
Yude Ji (Hebei Univ. of Science and Tech., China)
Abstract:
Using the Leggett-Williams fixed point theorem in cones,
we prove the existence of at least three
positive solutions to the nonlinear $n$-th order $m$-point
boundary-value problem
$$\displaylines{
\Delta^{n}u(k)+a(k)f(k,u)=0, \quad k\in \{0,N\},\cr
u(0)=0,\; \Delta u(0)=0, \dots, \Delta^{n-2}u(0)=0,\quad
u(N+n)=\sum_{i=1}^{m-2}\alpha_iu(\xi_i).
}$$
Submitted March 12, 2010. Published June 24, 2011.
Math Subject Classifications: 39A10.
Key Words: Boundary value problem; positive solution;
fixed point theorem; Green's function.