Mathematical Sciences: Faculty Publications
Locating the Peaks of Least Energy Solutions to a Quasilinear Ellitpic Neumann Problem
Document Type
Article
Publication Date
12-15-2007
Publication Title
Journal of Mathematical Analysis and Applications
DOI
10.1016/j.jmaa.2007.02.086
ISSN
0022-247X
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 ∂Ω achieves its maximum. We also give a complete proof of exponential decay of least-energy solutions.
Recommended Citation
Li, Yi, Chunshan Zhao.
2007.
"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
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/690
Copyright
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