The authors study a chemostat with a constant concentration of input nutrient and a time periodic washout rate. Using a global bifurcation theorem of P. H. Rabinowitz
[J. Funct. Anal. 7, 487-513 (1971; Zbl 0212.165
)], they establish the existence of a periodic solution, which corresponds to the coexistence of competitors, within appropriate parameter ranges. They also determine parameter regions where competitive exclusion holds.