The paper gave a slightly different version of the compact perturbations of maximal monotone operators due to A. G. Kartsatos [J. Math. Ann. 78, 1-16 (1980; Zbl 0447.47041)] and Chen Yongzhuo [Acta Math. Sin. 28, 140-144 (1985; Zbl 0571.47042)]. The author intended to apply his version to the nonlinear elliptic boundary value problem, but the assumption on the nonlinear term is very vague.