## 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^{m} Δ_{m} u - u^{m - 1} + f (u) = 0 with homogeneous Neumann boundary condition. In this paper we focus on the case 1 < m < 2 as a complement to our previous work on the case m ≥ 2. We use an intrinsic variation method to show that as the case m ≥ 2, when ε → 0^{+}, 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.

Original language | American English |
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Journal | Nonlinear Analysis: Theory, Methods & Applications |

Volume | 72 |

DOIs | |

State | Published - Jun 1 2010 |

## Keywords

- Exponential decay
- Least-energy solution
- Mean curvature
- Quasilinear Neumann problem
- m-Laplacian operator

## DC Disciplines

- Education
- Mathematics