Oberseminar Funktionalanalysis und partielle Differentialgleichungen
Feb262026
14:00
Lorenzo Giaretto: Least energy solutions for nonlinear Schrödinger system with K-wise
interactions and related free boundary problems
In the first part of this talk we discuss the existence and qualitative properties of least energy solutions for a weakly coupled nonlinear Schrödinger system with K-wise interaction, namely systems whose interaction term involves the product of all components. We consider both attractive and repulsive regimes and provide sufficient conditions on the competition parameter ensuring the existence of least energy fully non-trivial solutions, possibly under a radial symmetry constraint. We then investigate the asymptotic behavior of least energy fully non-trivial radial solutions in the strong competition limit. In this regime, we observe partial segregation phenomena which differ substantially from those arising in systems with pairwise interactions. In the final part of the talk, we consider a related system and establish Hölder bounds for least energy solutions that are uniform with respect to the competition parameter. We also discuss ongoing work concerning the regularity of the limiting problem and the associated free boundary. This talk is based on joint work with N. Soave
