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Article
On the Structure of Solutions to a Class of Quasilinear Elliptic Neumann Problems, Part II
Journal of Differential Equations
  • Chunshan Zhao, Georgia Southern University
  • Yi Li, University of Iowa
Document Type
Article
Publication Date
1-1-2010
DOI
10.1016/j.jde.2004.07.021
Disciplines
Abstract
We continue our work (Y. Li, C. Zhao in J Differ Equ 212:208–233, 2005) to study the structure of positive solutions to the equation εm Δmu − um−1 + f(u) = 0 with homogeneous Neumann boundary condition in a smooth bounded domain of RN (N ≥ 2). First, we study subcritical case for 2 < m < N and show that after passing by a sequence positive solutions go to a constant in C1, α sense as ε → ∞. Second, we study the critical case for 1 < m < N and prove that there is a uniform upper bound independent of ε ∈ [1, ∞) for the least-energy solutions. Third, we show that in the critical case for 1 < m ≤ 2 the least energy solutions must be a constant if ε is sufficiently large and for 2 < m < N the least energy solutions go to a constant in C1, α sense as ε → ∞.
Citation Information
Chunshan Zhao and Yi Li. "On the Structure of Solutions to a Class of Quasilinear Elliptic Neumann Problems, Part II" Journal of Differential Equations Vol. 37 Iss. 1-2 (2010) p. 237 - 258
Available at: http://works.bepress.com/chunshan_zhao/14/