Positive solutions of four-point boundary value problem for fourth order ordinary differential equation

Abstract

In this paper, the fourth order differential equation with four-point boundary value problem y ( 4 ) ( t ) − f ( t , y ( t ) , y ′ ′ ( t ) ) = 0 , 0 ≤ t ≤ 1 , y ( 0 ) = y ( 1 ) = 0 , a y ′ ′ ( ξ 1 ) − b y ′ ′ ′ ( ξ 1 ) = 0 , c y ′ ′ ( ξ 2 ) + d y ′ ′ ′ ( ξ 2 ) = 0 is studied, where 0 ≤ ξ 1 < ξ 2 ≤ 1 . Some sufficient conditions guaranteeing the existence of positive solution to the above four-point boundary value problem are obtained by using the Krasnosekii fixed point theorem.