On D.Y. Gao and R.W. Ogden's paper "Multiple solutions to non-convex   variational problems with implications for phase transitions and numerical   computation"
  In this note we prove that a recent result stated by D.Y. Gao and R.W. Ogden on global minimizers and local extrema in a phase transition problem is false. Our goal is achieved by providing a thorough analysis of the context and result in question and counter-examples. 
M.D. Voisei, C. Zalinescu
math.OC