For the simple shear problem of a perfectly elastoplastic body, we convert the non-linear governing equations into a third order linear differential system, then into a second order linear differential system, and further into a Sturm-Liouville equation. Thus Sturm's comparison theorem can be employed and extended to compare the simple shear responses based on different objective corotational stress rates. It is proved that the rates of Jaumann, Green-Naghdi, Sowerby-Chu, Xiao-Bruhns-Meyers, and Lee-Mallett-Wertheimer render non-oscillatory stress responses, with the Jaumann equation as a Sturm majorant for the other four equations. For an objective corotational stress rate with the general plane spin a sufficient non-oscillation criterion is found to be that the plane spin must not exceed the shear strain rate.