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- W2085671636 abstract "We study the behavior of finite Morse index solutions of the equation−Δu=|x|α|u|p−1uin Ω⊂RN, where p>1, α>−2, and Ω is a bounded or unbounded domain. We show that there is a critical power p=p¯(α) larger than the usual critical exponent N+2N−2 such that this equation with Ω=RN has no nontrivial stable solution for 1<p<p¯(α) but it admits a family of stable positive solutions when p⩾p¯(α). For a positive solution u with finite Morse index, we classify the singularity of u at the origin when Ω is a punctured ball BR(0){0}, and we classify its behavior at infinity when Ω=RN∖BR(0). We show that the behavior depends crucially on whether p is below or above the critical power p¯(α). We also demonstrate how a duality method can be used to obtain sharper results." @default.
- W2085671636 created "2016-06-24" @default.
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- W2085671636 date "2011-04-01" @default.
- W2085671636 modified "2023-10-03" @default.
- W2085671636 title "Finite Morse index solutions of an elliptic equation with supercritical exponent" @default.
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- W2085671636 doi "https://doi.org/10.1016/j.jde.2011.02.005" @default.
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