Multi-bump solutions for critical Schrödinger equations with electromagnetic fields and logarithmic nonlinearity

In this paper, we are interested in the existence and multiplicity of multi-bump solutions for critical Schrödinger equations with electromagnetic fields and logarithmic nonlinearity of the following type: [Formula: see text] where [Formula: see text], the magnetic potential [Formula: see text] the parameter [Formula: see text] and [Formula: see text] are the non-negative continuous functions. Applying variational methods, we obtain that the above equations have at least [Formula: see text] multi-bump solutions as [Formula: see text] is sufficiently large. To some extent, we extend and complement the results of [C. O. Alves and C. Ji, Multi-bump positive solutions for a logarithmic Schrödinger equation with deepening potential well, Sci. China Math. 65 (2022) 1577–1598; J. Wang and Z. Yin, Multi-bump solutions for the nonlinear magnetic Schrödinger equation with logarithmic nonlinearity, Math. Nachr. 298 (2025) 328–355] from subcritical case to critical case.