Existence of positive solutions for a fourth-order differential system (Q2925547)

The authors investigate the existence of positive solutions for a fourth-order differential system NEWLINE\[NEWLINE\begin{gathered} u^{(4)}=\varphi u+f(t,u,u''),\quad -\varphi''=\mu u,\;\;0<t<1, \\ u(0)=u(1)=u''(0)=u''(1)=0, \quad \varphi(0)=\varphi(1)=0\end{gathered}NEWLINE\]NEWLINE by using a fixed point theorem of cone expansion and compression type. They obtain existence and multiplicity results under some suitable conditions.