Normalized solutions for critical Schrodinger-Bopp-Podolsky systems with p -Laplacian and competing potentials

The paper deals with the following critical Schrödinger-Bopp-Podolsky system [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text] is the Bopp-Podolsky constant, [Formula: see text] appears as a Lagrange multiplier, [Formula: see text], [Formula: see text] is the Sobolev critical exponent, [Formula: see text] is the [Formula: see text]-Laplace operator, the absorption potential [Formula: see text] and the reaction potential [Formula: see text] are continuous functions, and [Formula: see text] is a continuous function with subcritical growth at infinity. To our best knowledge, this paper is the first study on normalized solutions for a Schrödinger-Bopp-Podolsky system involving the [Formula: see text]-Lapalcian, the Sobolev critical exponent and competing potentials. With the aid of minimization techniques and the Lusternik-Schnirelmann category theory, the existence, concentration, multiplicity and nonexistence of normalized solutions for system [Formula: see text] are obtained. To some extent, our main theorems complement and extend the results of Alves and Thin in [4] (SIAM J. Math. Anal. 55: 1264–1283, 2023), D’Avenia and Siciliano in [12] (J. Differential Equations 267: 1025–1065, 2019), Santos et al. in [35] (Calc. Var. Partial Differential Equations 63: Paper No. 155, 2024) and Zhang et al. in [41] (Math. Z. 301: 4037–4078, 2022).