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In this short paper I report on a paper published in Nonlinear Analysis: RealWorld Applications in 2004. There is a major mistake early in that paper whichmakes most of its claims false. The class of reaction-diffusion systemsconsidered in the paper has been the object of a renewed investigation in thepast few years, by myself and others, and recent discoveries provide explicitcounterexamples .

A note on "Existence and uniqueness of coexistence states for an  elliptic system coupled in the linear part", by Hei Li-Jun, Nonlinear Anal.  Real World Appl. 5, 2004