Locating the Peaks of Least-Energy Solutions to a Quasi-Linear Elliptic Neumann Problem, Part II

Authors

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

Document Type

Article

Publication Date

6-1-2010

Publication Title

Nonlinear Analysis: Theory, Methods & Applications

DOI

10.1016/j.na.2010.01.049

ISSN

0362-546X

Abstract

We continue our work (Y. Li, C. Zhao, Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem, J. Math. Anal. Appl. 336 (2007) 1368–1383) to 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. In this paper we focus on the case 1+, the global maximum point P_ε of least-energy solutions goes to a point on the boundary ∂Ω at a rate of o(ε) and this point on the boundary approaches a global maximum point of mean curvature of ∂Ω.

Recommended Citation

Zhao, Chunshan, Yi Li. 2010. "Locating the Peaks of Least-Energy Solutions to a Quasi-Linear Elliptic Neumann Problem, Part II." Nonlinear Analysis: Theory, Methods & Applications, 72 (11): 4188-4199. doi: 10.1016/j.na.2010.01.049
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/246