The dc potential solutions which have zero slope at the emitter are calculated and examined for the low‐pressure cesium diode. It is assumed that ions and electrons are emitted thermionically at the emitter with a given ratio of ion‐to‐electron saturation currents and a positive dc potential is applied to the collector. Furthermore, the potential is nowhere negative in the diode and electron saturation current flows through it. This assumption limits the range of &agr;'s to 0<&agr;<1, where &agr; is the ratio of ion‐to‐electron saturation currents times the square root of the ratio of their masses. It was found by Auer and Hurwitz that monotonically increasing potential solutions can exist only for the range of &agr;'s, 0<&agr;<0.405. In the range 0.35<&agr;<0.405 we found large amplitude oscillations in the diode by computer simulation methods. The static solutions for &agr;<0.35 were found stable. For 1>&agr;>0.405 the static potential solutions have a long zero slope region within the diode or become periodic in space. All these solutions were found unstable and nonexistent in the diode that operates under time‐varying conditions just as predicted by Auer and Hurwitz.