Article
On the Structure of Solutions to a Class of Quasilinear Elliptic Neumann Problems
Journal of Differential Equations
(2005)
Abstract
We study the structure of positive solutions to the equation ɛmΔmu -um-1+fu=0 with homogeneous Neumann boundary condition. First, we show the existence of a mountain-pass solution and find that as ɛ→0+ the mountain-pass solution develops into a spike-layer solution. Second, we prove that there is an uniform upper bound independent of ɛ for any positive solution to our problem. We also present a Harnack-type inequality for the positive solutions. Finally, we show that if 1<m⩽2 holds and ɛ is sufficiently large, any positive solution must be a constant.
Keywords
- Quasilinear Neumann Problem,
- M-laplacian Operator,
- Mountain-pass Solution,
- Least-energy Solution,
- Spike-layer Solution,
- Harnack Inequality
Disciplines
Publication Date
May, 2005
DOI
10.1016/j.jde.2004.07.021
Citation Information
Yi Li and Chunshan Zhao. "On the Structure of Solutions to a Class of Quasilinear Elliptic Neumann Problems" Journal of Differential Equations Vol. 212 Iss. 1 (2005) p. 208 - 233 ISSN: 0022-0396 Available at: http://works.bepress.com/chunshan_zhao/28/