Abstract:

The nonlocal boundary value problem for a nonlinear fourth-order ordinary differential equation is considered. The existence of positive soluations is shown to the problem above by applying a generalization of the cone expansion and compression fixed point theorem. In order to study this problem, cone and convex functional are introduced. This method is different from others which discussed the existence of positive solutions about the problem.

Key words: nonlocal boundary value problems; positive solutions; cone expansion compression; convex functional; cone