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Article
Locating the Peaks of Least-Energy Solutions to a Quasi-Linear Elliptic Neumann Problem
Journal of Mathematical Analysis and Applications
  • Chunshan Zhao, Georgia Southern University
  • Yi Li, The University of Iowa
Document Type
Article
Publication Date
1-1-2010
DOI
10.1016/j.jmaa.2007.02.086
Disciplines
Abstract
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 ∂Ωachieves its maximum. We also give a complete proof of exponential decay of least-energy solutions.
Citation Information
Chunshan Zhao and Yi Li. "Locating the Peaks of Least-Energy Solutions to a Quasi-Linear Elliptic Neumann Problem" Journal of Mathematical Analysis and Applications Vol. 72 Iss. 11 (2010) p. 4188 - 4199
Available at: http://works.bepress.com/chunshan_zhao/16/