In this note, we consider the Hotelling model with linear transportation costs. We show that capacity constraints may restore the existence of an equilibrium for locations inside the first and third quartiles.
Wauthy, X. (1996). Capacity constraints may restore the existence of an equilibrium in the Hotelling model. Journal of Economics, 64(3), 315-324. https://doi.org/10.1007/BF01250131 (Original work published 1996)