Recently, the max-min approach was systematically studied in the review article (Ji-Huan, 2012). This paper concludes that He's max-min approach is also a very much effective method for nonlinear oscillators with discontinuous terms.
"He's Max-Min Approach to a Nonlinear Oscillator with Discontinuous Terms." Abstr. Appl. Anal. 2013 1 - 2, 2013. https://doi.org/10.1155/2013/579731