The purpose of the present paper is to give a proof for a systematic method namely, predictor
homotopy analysis method (PHAM) to predict the multiplicity of the solutions of
two points nonlinear second order boundary value problems of type u′′ = f
x, u, u′
. We
present briefly the method first, and then some theorems are given to clarify this issue
that, how one can predict the existence of the multiple solutions and obtain them simultaneously
as well.
