Mathematical Sciences: Faculty Publications
On the Structure of Solutions to a Class of Quasilinear Elliptic Neumann Problems, Part II
Document Type
Article
Publication Date
1-2010
Publication Title
Calculus of Variations and Partial Differential Equations
DOI
10.1007/s00526-009-0261-2
ISSN
1432-0835
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 → ∞.
Recommended Citation
Zhao, Chunshan, Yi Li.
2010.
"On the Structure of Solutions to a Class of Quasilinear Elliptic Neumann Problems, Part II."
Calculus of Variations and Partial Differential Equations, 37 (1-2): 237-258.
doi: 10.1007/s00526-009-0261-2
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/247
Copyright
This work is archived and distributed under the repository's Standard Copyright and Reuse License (opens in new tab). End users may copy, store, and distribute this work without restriction. For all other uses, permission must be obtained from the copyright owners or their authorized agents.
