Multiple positive solutions for boundary value problems of second-order delay differential equations

Abstract

We use a fixed-point index theorem in cones to study the existence of multiple positive solutions for boundary value problems of second-order delay differential equations with the form y″(x) + ƒ(x,y(x − τ)) = 0, 0 < x < 1, y(x) = 0, −τ ≤ x ≤ 0, y(1) = 0, where 0 < τ < 1 4 is suitably small. The main result here is the generalization of Liu and Li [1] for ordinary differential equations.