On weakly coupled elliptic systems with critical growth
摘要：In this talk, we are concerned with positive vector solutions of Bose-Einstein type systems in dimension four and two. The interaction is critical in the sense of Sobolev in dimension four and of critical exponential type in the sense of Moser in dimension two. In dimension four, via the Hopf fi
bration approach, concentration phenomena around spheres are investigated in the attractive case as the Planck constant goes to zero. As for dimension two, we prove, using variational methods, the existence of positive vector ground state solutions both in the attractive and repulsive cases. This talk is based on joint work with Joao Marcos do O and with Daniele Cassani and Hugo Tavares.