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This paper is concerned with a general chemical reaction model with respect to Neumann boundary condition. The stability of positive equilibrium and the non-existence of non-constant positive solution are discussed rigorously, respectively in Case 1: f (u) > 0 and fu(u) < 0 for u > 0 and Case 2: f (0) = 0 and fu(u) > 0 for u > 0. The techniques include the spectrum analysis of operators, the maximal principle, the upper and lower solution method and the implicit function theorem.

Analysis on stability and non-existence of equilibrium for a general chemical reaction