Locating the Peaks of Least-energy Solutions to a Quasilinear Elliptic Neumann Problem

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Abstract

We will study the shape of least-energy solutions to the quasilinear problem εm∆mu−um−1 +f(u) = 0 with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that as ε → 0, the point Pε ∈ ∂Ω where least-energy solution achieves its maximum goes to a point where the mean curvature of ∂Ω achieves its maximum. We also give a complete proof of exponential decay of least-energy solutions. Even for case m=2 our proof is an extension of earlier ones in that the non-degeneracy of the ground state is not required here in our work.
Original languageAmerican English
StatePublished - Oct 22 2005
EventFall Central Sectional Meeting of the American Mathematical Society (AMS) - Lincoln, NE
Duration: Oct 15 2011 → …

Conference

ConferenceFall Central Sectional Meeting of the American Mathematical Society (AMS)
Period10/15/11 → …

Disciplines

  • Mathematics

Keywords

  • Peaks of Least-energy Solutions
  • Quasilinear Elliptic Neumann Problem

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