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In this note we prove that a recent result stated by D.Y. Gao and R.W. Ogdenon 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 resultin question and counter-examples.

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"