Locating the Peaks of Least-Energy Solutions to a Quasilinear Elliptic Neumann Problem
In this paper we study the shape of least-energy solutions to a singularly perturbed quasilinear problem with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that at limit, the global maximum point of least-energy solutions goes to a point on the boundary faster than the linear rate and this point on the boundary approaches to a point where the mean curvature of the boundary achieves its maximum. We also give a complete proof of exponential decay of least-energy solutions.
& Zhao, C.
(2007). Locating the Peaks of Least-Energy Solutions to a Quasilinear Elliptic Neumann Problem. Journal of Mathematical Analysis and Applications, 336 (2), 1368-1383.