Concentration phenomenon of semiclassical states to reaction-diffusion systems

In this paper, we consider concentration phenomenon of semiclassical states to the following 2M-component reaction-diffusion system in R x R-N, {& part;(t)u = epsilon(2)delta(x)u - u - V(x)v + & part;(v) H(u, v),& part;(t)v = -epsilon(2)delta(x)v + v + V(x)u - & part;(u) H(u, v), where M >= 1, N >= 1, epsilon > 0 is a small parameter, V is an element of C-1(R-N, R), H is an element of C-1(R-M x R-M, R) and (u, v) : R x R-N -> R-M x R-M. It is proved that there exist semiclassical states concentrating around the local minimum points of V under mild assumptions. The approach is variational, which is mainly based upon a new linking-type argument, iterative techniques and interior estimates for nonlinear parabolic equations.