On the role of the equal-area condition in internal layer
stationary solutions to a class of reaction-diffusion systems

Janete Crema, Arnaldo Simal do Nascimento
Abstract:
We present necessary conditions for the formation of internal
transition layers in stationary solutions to some singularly
perturbed reaction-diffusion systems.  In particular we prove that
the well-known equal-area condition which is always assumed in a
typical set of sufficient conditions for existence of such
solutions is actually a necessary hypothesis.  Examples of
existence and nonexistence of these solutions are given.