Minimal coexistence configurations for multispecies systems
  We deal with strongly competing multispecies systems of   Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows indefinitely, the system reaches a state of coexistence of all the species in spatial segregation. Furthermore, the limit configuration is a local minimizer for the associated free energy. 
Monica Conti and Veronica Felli