Existence and multiplicity of positive solutions of a fourth-order
m-piont BVP with sign-changing Green's function
Abstract
In this paper, we study the fourth-order m-point boundary value problem
\begin{equation*} \left
\{\begin{array}{lcr}
u^{(4)}(t)=f(t,u(t)),\ t\in
[0,1],\\ u’(0)=u’‘(0)=u(1)=0 ,
u’‘(1)-\sum^{m-2}_{i=1}\alpha_i
u”’(\xi_i)=0,
\end{array}\right.
\end{equation*} with sign-changing Green’s function. By
using some fixed theorems and the properties of Green’s function, we
mainly establish the existence and multiplicity of positive solution for
the problems under some suitable conditions.