High-energy and multi-peaked solutions for a nonlinear neumann problem with critical exponents

Abstract

We establish the existence of positive solutions with two peaks being located on the boundary of the domain for the problem -Δu + λu = up in antipodal invariant domains including ball domains with Neumann boundary conditions. Here p is the critical Sobolev exponent (N + 2)/(N - 2). The shape of the solutions and the location of the peaks are also studied. © 1995, Royal Society of Edinburgh. All rights reserved.