Multi-peak Solutions for a Singularly Perturbed Semilinear Elliptic Problem

AbstractThis paper is concerned with the existence of multi-peak solutions of the following problem[formula] where Ω is a smooth bounded domain in RN (N⩾2), ε>0 is a small positive number and p∈(2, 2NN−2) for N⩾3, p∈(2, +∞) for N=2. Using a variational method we construct positive solutions concentrating near given “saddle points” of the distance function dist(·, ∂Ω). An explicit expression for the dominant parts of the solutions is also obtained