Normalized solutions of critical Schrödinger system involving fractional p-Laplacian

In this paper, we study the normalized solutions of the following critical Schrödinger system involving fractional [Formula: see text]-Laplacian: [Formula: see text] under the constraints [Formula: see text] where [Formula: see text] is a parameter, [Formula: see text] is the fractional [Formula: see text]-Laplace operator, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text] are prescribed, [Formula: see text] are unknown parameters, and the potential functions [Formula: see text] are continuous. For the [Formula: see text]-subcritical case, we obtain the multiple normalized solutions by truncation technique and Lusternik–Schnirelmann category theory. For the [Formula: see text]-supercritical case, we show the existence of a normalized solution by developing the auxiliary functional. For both cases, with the aid of the concentration compactness principle, we overcome the loss of compactness of the energy functional caused by the critical growth. Our main conclusions extend and/or complement some results established by Alves and Thin [SIAM J. Math. Anal. 55 (2023) 1264–1283], Gou and Jeanjean [Nonlinearity 31 (2018) 2319–2345], and Tong, Van Nguyen and Liang [Commun. Nonlinear Sci. Numer. Simul. 144 (2025) 108665].