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

Abstract

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.