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 language | American English |
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State | Published - Oct 22 2005 |
Event | Fall Central Sectional Meeting of the American Mathematical Society (AMS) - Lincoln, NE Duration: Oct 15 2011 → … |
Conference
Conference | Fall Central Sectional Meeting of the American Mathematical Society (AMS) |
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Period | 10/15/11 → … |
Disciplines
- Mathematics
Keywords
- Peaks of Least-energy Solutions
- Quasilinear Elliptic Neumann Problem