Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity

Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the ‐Laplace operator and a logarithmic nonlinearity: The analysis is developed under the prescribed mass assumption , where , , and . The potential is a bounded and continuous function that satisfies some suitable global conditions. The main results establish the existence, multiplicity and concentration of normalized solutions to the above system and the proofs combine suitable variational and topological methods. This seems to be the first paper dealing with the existence and concentration of solutions with prescribed mass for critical Schrödinger–Bopp–Podolsky systems involving the ‐Laplacian and logarithmic nonlinearity. In the final part of this paper, we are interested in the asymptotic behavior of normalized solutions as and , respectively. The main feature of this paper is given by the combined effects generated by the simultaneous appearance of a quasilinear operator, critical exponent, and the logarithmic nonlinearity.