Normalized solutions to the Kirchhoff equation with L2-subcritical or critical nonlinearities in R2

In this paper, we study the existence of normalized solutions to the Kirchhoff equation with L-2- subcritical or critical nonlinearities - (a + b integral R-2 |& nabla;u|(2)dx) delta u = lambda u + |u|(p-2)u + mu|u|(q-2)u in R-2,where a, b, mu > 0, 2 < q < p <= 6. By minimizing methods and the concentration compactness principle, we prove the existence and nonexistence of normalized solutions when (p, q) belongs to a certain domain in R-2, and discuss how mu affects the existence of normalized solutions. Our main results may be illustrated by the red areas and green areas shown in Figure 1. Our results partially extend the results of Soave (J. Differ. Equ. 2020).