Solutions with interior and boundary peaks for the Neumann problem of an elliptic system of FitzHugh-Nagumo type E. DancerShusen Yan 35J5093C15nonlinear boundary value problemssmall diffusion We study the existence of peak solutions for the Neumann problem of an elliptic system of FitzHugh-Nagumo type. The solutions we construct have arbitrary many peaks on the boundary and arbitrary many peaks inside the domain, and all the peaks of the solutions approach some local minimum points of the mean curvature function of the boundary. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2614 10.1512/iumj.2006.55.2614 en Indiana Univ. Math. J. 55 (2006) 217 - 258 state-of-the-art mathematics http://iumj.org/access/