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).