Title

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.

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