Positive solutions for boundary value problems of functional differential equations

Abstract

We study the existence of positive solutions of the second order boundary values problems of functional differential equations x ″ ( t ) + f ( t , x t ) = 0 , 0 < t < T , x 0 = φ , x ( T ) = A , where f : [ 0 , T ] × C r → R is a continuous function, φ ∈ C r ( : = C [ - r , 0 ] ) and A ∈ R . The proof of our main result is based upon the fixed point theorem in cones.