Abstract

In this article we construct a new type of solutions for the Gierer and Meinhardt system -ε2uxx + u &=&u 2/v in (0,L),- vxx+ v &=& u2 in (0, L) with boundary conditions u x (0) = u x (L) = 0 and v x (0) = v x (L) = 0. As ε approaches zero, we construct a family of positive solution (u ε , v ε ) such that the activator u ε oscillates c 0/ε times, with c 0 in an appropriate range, while the inhibitor remains close to a limiting profile, which is a strictly decreasing function. © 2007 Springer-Verlag.