Abstract:
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.