On the Shape of Least-Energy Solutions for a Class of Quasilinear Elliptic Neumann Problems

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We study the shape of least-energy solutions to the quasilinear elliptic equation εm Δmu - um-1 + f(u) = 0 with homogeneous Neumann boundary condition as ε → 0+ in a smooth bounded domain Ω ⊂ ℝN. Firstly, we give a sharp upper bound for the energy of the least-energy solutions as ε → 0+, which plays an important role to locate the global maximum. Secondly, based on this sharp upper bound for the least energy, we show that the least-energy solutions concentrate on a point Pε and dist (Pε ∂Ω)/ε goes to zero as ε → 0+. We also give an approximation result and find that as ε → 0+ the least-energy solutions go to zero exponentially except a small neighbourhood with diameter O(ε) of Pε where they concentrate.

Original languageAmerican English
JournalIMA Journal of Applied Mathematics
Volume72
DOIs
StatePublished - Apr 1 2007

Keywords

  • Least-Energy Solution
  • M-Laplacian Operator
  • Quasi-Linear Neumann Problem

DC Disciplines

  • Education
  • Mathematics

Fingerprint

Dive into the research topics of 'On the Shape of Least-Energy Solutions for a Class of Quasilinear Elliptic Neumann Problems'. Together they form a unique fingerprint.

Cite this