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- W2000603684 abstract "We study positive solutions of the equationΔu=|x|αu−pin Ω⊂RN(N⩾2), where p>0, α>−2, and Ω is a bounded or unbounded domain. We show that there is a critical power p=pc(α) such that this equation with Ω=RN has no stable positive solution for p>pc(α) but it admits a family of stable positive solutions when 0<p⩽pc(α). If p>pc(α−) (α−=min{α,0}), we further show that this equation with Ω=Br∖{0} has no positive solution with finite Morse index that has an isolated rupture at 0, and analogously it has no positive solution with finite Morse index when Ω=RN∖BR. Among other results, we also classify the positive solutions over Br∖{0} which are not bounded near 0." @default.
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- W2000603684 date "2009-03-01" @default.
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- W2000603684 title "Positive solutions of an elliptic equation with negative exponent: Stability and critical power" @default.
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- W2000603684 doi "https://doi.org/10.1016/j.jde.2008.08.008" @default.
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