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- W2565836089 abstract "In this paper, we study the singular behavior at x=0 of positive solutions to the equation−Δu=λ|x|2u−|x|σup,x∈Ω{0}, where Ω⊂RN(N≥3) is a bounded domain with 0∈Ω, and p>1, σ>−2 are given constants. For the case λ≤(N−2)2/4, the singular behavior of all the positive solutions is completely classified in the recent paper [5]. Here we determine the exact singular behavior of all the positive solutions for the remaining case λ>(N−2)2/4. In sharp contrast to the case λ≤(N−2)2/4, where several converging/blow-up rates of u(x) are possible as |x|→0, we show that when λ>(N−2)2/4, every positive solution u(x) blows up in the same fashion:lim|x|→0|x|2+σp−1u(x)=[λ+2+σp−1(2+σp−1+2−N)]1/(p−1)." @default.
- W2565836089 created "2017-01-06" @default.
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- W2565836089 date "2017-04-01" @default.
- W2565836089 modified "2023-09-23" @default.
- W2565836089 title "Exact singular behavior of positive solutions to nonlinear elliptic equations with a Hardy potential" @default.
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- W2565836089 doi "https://doi.org/10.1016/j.jde.2016.12.004" @default.
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