Locating the Peaks of Least Energy Solutions to a Quasilinear Ellitpic Neumann Problem

Authors

Yi Li, The University of IowaFollow
Chunshan Zhao, Georgia Southern UniversityFollow

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 ε^mΔ_mu−u^m−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 P_ε 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