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"

Abstract

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.