Dans cet article nous montrons lʼexistence dʼune infinité de solutions qui changent de signe pour le système dʼéquations de Schrödinger avec des interactions compétitives où Ω est un domaine borné, et ∀i. De plus, quand , nous démontrons une relation entre les énergies critiques associées à ce système et le problème de partition optimale où indiques la -ème valeur propre de lʼopérateur −Δ in . Dans le cas , nous montrons que le problème de partition optimale apparaît comme une valeur limite critique, en tant que paramètre de compétition β diverge vers +∞.
In this paper we prove the existence of infinitely many sign-changing solutions for the system of m Schrödinger equations with competition interactions where Ω is a bounded domain, and ∀i. Moreover, for , we show a relation between critical energies associated with this system and the optimal partition problem where denotes the -th eigenvalue of −Δ in . In the case we show that the optimal partition problem appears as a limiting critical value, as the competition parameter β diverges to +∞.
@article{AIHPC_2012__29_2_279_0, author = {Tavares, Hugo and Terracini, Susanna}, title = {Sign-changing solutions of competition--diffusion elliptic systems and optimal partition problems}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {29}, year = {2012}, pages = {279-300}, doi = {10.1016/j.anihpc.2011.10.006}, mrnumber = {2901198}, zbl = {1241.35046}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2012__29_2_279_0} }
Tavares, Hugo; Terracini, Susanna. Sign-changing solutions of competition–diffusion elliptic systems and optimal partition problems. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) pp. 279-300. doi : 10.1016/j.anihpc.2011.10.006. http://gdmltest.u-ga.fr/item/AIHPC_2012__29_2_279_0/
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