Concentration and asymptotics of normalized solutions to the critical Schrödinger-Bopp-Podolsky system in ℝ ³

We study the following critical Schrödinger-Bopp-Podolsky system with competing nonlinearities [Formula: see text] and prescribed mass [Formula: see text] where [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text]. The potential [Formula: see text] is a bounded and continuous nonnegative function, satisfying some suitable global conditions. The main feature of this paper consists in the competing effects of critical terms, nonlocal terms, and potential functions. To address this issue, the concentration-compactness principle is needed to overcome the loss of compactness of the energy functional due to critical growth. Meanwhile, by using the minimization techniques and the truncated argument, we show that the number of normalized solutions is not less than the number of global minimum points of [Formula: see text] when the parameter [Formula: see text] is sufficiently small. Furthermore, we study the asymptotic behaviors of normalized solutions as [Formula: see text] and as [Formula: see text], respectively. To the best of our knowledge, this study seems to be the first contribution regarding the concentration and asymptotic behavior for Schrödinger-Bopp-Podolsky systems.