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

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.