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. © 2009 Elsevier Ltd. All rights reserved.
Conti, M., & Felli, V. (2009). Minimal coexistence configurations for multispecies systems. Nonlinear Analysis, Theory, Methods and Applications, 71(7–8), 3163–3175. https://doi.org/10.1016/j.na.2009.01.225