We consider an optimal partition problem in N-dimensional domains related to a method introduced by Nehari. We prove existence of the minimal partition and some extremality conditions. Moreover we show some connections between the variational problem, the behaviour of competing species systems with large interaction and changing sign solutions to elliptic superlinear equations. © 2002 Éditions scientifiques et médicales Elsevier SAS.
Conti, M., Terracini, S., & Verzini, G. (2002). Nehari’s problem and competing species systems. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire, 19(6), 871–888. https://doi.org/10.1016/S0294-1449(02)00104-X