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
NSF; Division of Mathematical Sciences 9201283
NSF, Division of Mathematical Sciences
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.