Abstract: We study stationary solutions of the neuronal field equation, a nonlinear integro-differential equation of the Hammerstein type. This equation models the behaviuor of a single layer of neurons in human cortex. The talk is mainly concerned with the existence of stationary bumps, that is, stationary spatially localised solutions. Their Lyapunov stability will be discussed as well. The talk is based on a joint work with Anna Oleynik (Uppsala).