Rainer Mandel  pointed out a mistake about Remark 3.1 (i) on page 654 in , which was published in Tohoku Mathematics Journal, Vol. 63, 2011. Here and hereafter, the numbers of formulas, theorems, sections and pages correspond to those in the paper  except for (C1), (C2), (C3) and (C4) below.
"Erratum: Stability of stationary solution for the Lugiato-Lefever equation." Tohoku Math. J. (2) 72 (3) 487 - 492, 2020. https://doi.org/10.2748/tmj/1601085626