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.