Necessary and sufficient conditions for the existence of positive solutions of fourth order multi-point boundary value problems

This paper investigates the existence of positive solutions of singular multi-point boundary value problems of fourth order ordinary differential equation with pp-Laplacian. A necessary and sufficient condition for the existence of C2[0,1]C2[0,1] positive solution as well as pseudo  -C3[0,1]C3[0,1] positive solution is given by means of the fixed point theorems on cones.