Positive solutions for nonlinear fourth order boundary value problems in ordered Banach spaces

The existence of positive solutions for nonlinear fourth order boundary value problem \left\\beginarrayll u^(4)(t)=f(t,u(t),u''(t)),\qquad 0\leqslant t\leqslant 1, \\ u(0)=u(1)=u''(0)=u''(1)=\theta, \\ \endarray \right. in an ordered Banach space \ E is discussed, where \ f:0, 1\times E\times E \rightarrow E is continuous. Under more general conditions of noncompactness measure and semi-ordering, an existence result of positive solutions is obtained by employing the fixed point index theory of condensing mapping.