Locating the Peaks of Least Energy Solutions to a Quasilinear Ellitpic Neumann Problem
Journal of Mathematical Analysis and Applications
In this paper we study the shape of least-energy solutions to the quasilinear problem εmΔmu−um−1+f(u)=0 with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that as ε→0+, the global maximum point Pε of least-energy solutions goes to a point on the boundary ∂Ω at the rate of o(ε) and this point on the boundary approaches to a point where the mean curvature of ∂Ω achieves its maximum. We also give a complete proof of exponential decay of least-energy solutions.
Li, Yi, Chunshan Zhao.
"Locating the Peaks of Least Energy Solutions to a Quasilinear Ellitpic Neumann Problem."
Journal of Mathematical Analysis and Applications, 336 (2): 1368-1383.
doi: 10.1016/j.jmaa.2007.02.086 source: https://www.sciencedirect.com/science/article/pii/S0022247X07002302?via%3Dihub