2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210543We 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.Analysis of PDEs35J55, 47J30, 92D25text