TRIPLE JUNCTION SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM

Abstract

We consider the singularly perturbed Neumann problem epsilon(2)Delta u - u + up = 0, u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where p > 1 and Omega is a smooth and bounded domain in R-2. We construct a class of solutions which consist of large number of spikes concentrated on three line segments with a common endpoint which intersect partial derivative Omega orthogonally.