Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem |
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Authors: | Yi Li Chunshan Zhao |
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Institution: | a Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA b Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA |
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Abstract: | In this paper we study the shape of least-energy solutions to the quasilinear problem εmΔmu−um−1+f(u)=0 with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that as ε→0+, the global maximum point Pε of least-energy solutions goes to a point on the boundary ∂Ω at the rate of o(ε) and this point on the boundary approaches 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. |
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Keywords: | Quasilinear Neumann problem m-Laplacian operator Least-energy solution Exponential decay Mean curvature |
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