Article
Locating the Peaks of Least-Energy Solutions to a Quasilinear Elliptic Neumann Problem
Journal of Mathematical Analysis and Applications
Document Type
Article
Publication Date
1-1-2007
Disciplines
Abstract
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.
Citation Information
Yi Li and Chunshan Zhao. "Locating the Peaks of Least-Energy Solutions to a Quasilinear Elliptic Neumann Problem" Journal of Mathematical Analysis and Applications Vol. 336 Iss. 2 (2007) p. 1368 - 1383 ISSN: 0022-247X Available at: http://works.bepress.com/yi_li/27/