In this paper, we investigate the multiplicity and concentration of normalized solutions to a fractional Kirchhoff–Schrödinger problem with logarithmic nonlinearity. By combining the Pohozaev identity, the penalization technique, and the concentration–compactness principle, we overcome the twofold difficulties caused by the Kirchhoff term and the logarithmic nonlinearity and establish the validity of the (PS) condition. On this basis, we employ the Ljusternik–Schnirelmann category theory to prove the multiplicity of solutions, linking the number of solutions to the topological category of the set M in which the potential function V(x) attains its minimum. Finally, we analyze the concentration behavior and algebraic decay properties of these normalized solutions as ε→0.
Jin et al. (Mon,) studied this question.