The existence and the concentration behavior of normalized solutions for the L2-critical Schrödinger-Poisson system

As such constrained problem is L2-critical, E(u) is unbounded from below on S(c) when c>c∗ and the existence of critical points constrained on S(c) is obtained by a mountain pass argument on S(c). We show that there exists c1>(97)34c∗ such that E(u) has at least one positive critical point restricted to S(c) for c∗