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arXiv · 0704.0402

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

Yi Li·Chunshan Zhao
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Abstract

In this paper we study the shape of least-energy solutions to a singularly perturbed quasilinear problem with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that at limit, the global maximum point of least-energy solutions goes to a point on the boundary faster than the linear rate and this point on the boundary approaches to a point where the mean curvature of the boundary achieves its maximum. We also give a complete proof of exponential decay of least-energy solutions.

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Yi Li, Chunshan Zhao. 2007-04-03. Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem. https://doi.org/10.1093/imamat%2Fhxl032

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