ON THE INTERIOR SPIKE LAYER SOLUTIONS TO A SINGULARLY PERTURBED NEUMANN PROBLEM

Abstract

In this paper, we construct interior spike layer solutions for a class of semilinear elliptic Neumann problems which arise as stationary solutions of Keller-Segel model in chemotaxis and also as limiting equations for the Gierer-Meinhardt system in biological pattern formation. We also classify the locations of single interior peaks. We show exactly how the geometry of the domain affects the spike solutions.