On the Existence of Unstable Bumps in Neural Networks
  We study the neuronal field equation, a nonlinear integro-differential equation of Hammerstein type. By means of the Amann three fixed point theorem we prove the existence of bump solutions to this equation. Using the Krein-Rutman theorem we show their Lyapunov instability. 
Vadim Kostrykin and Anna Oleynik
math.DS math.FA