Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem

[摘要] In this paper we study the shape of least-energy solutions to the quasilinear problem epsilon(m) Delta(m)u - u(m-1) + f(u) = 0 with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that as epsilon -> 0(+), the global maximum point P-epsilon of least-energy solutions goes to a point on the boundary a partial derivative Omega at the rate of o(epsilon) and this point on the boundary approaches to a point where the mean curvature of partial derivative Omega achieves its maximum. We also give a complete proof of exponential decay of least-energy solutions. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] quasilinear neumann problem;m-Laplacian operator;least-energy solution;exponential decay;mean curvature