By using a fixed point theorem of mixed monotone operators in cone, this paper studied a fourth-order nonlinear singular boundary value problem, namely a class of elastic beam equation.

The shooting method, sub and super solution method, and fixed point theorem were used to study a class of nonlinear diffusion equations with nonlocal boundary value condition in perforated domains.

By using the fixed point theory and a new three-solution theorems, the existence of multiple solutions of the boundary value problem was obtained.