Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem

The purpose of this paper is to investigate the existence of symmetric positive solutions for a class of fourth-order boundary value problem: {y(4)(t)=f(t,y(t)),t∈[0,1],y(0)=y(1)=y′(0)=y′(1)=0. By using a monotone iterative technique, we proved that the above boundary value problem has symmetric positive solutions under certain conditions. In particular these solutions are obtained via the iteration procedures.