High-energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponents
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Cambridge University Press
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.
Wang, Zhi-Qiang, "High-energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponents" (1995). Mathematics and Statistics Faculty Publications. Paper 210.