We study entire positive solutions to the partial differential equa- tion in Rn , n+2 ∆x u + (α + 1)2 |x|2α ∆y u = −|x|2α u n−2 , where x ∈ R 2 , y ∈ Rn−2 , n ≥ 3 and α > 0. We classify positive solutions with second order derivatives satisfying a suitable growth near the set x = 0.
Positive solutions of anisotropic Yamabe-type equations in $Bbb Rsp n$
MONTI, ROBERTO;
2008
Abstract
We study entire positive solutions to the partial differential equa- tion in Rn , n+2 ∆x u + (α + 1)2 |x|2α ∆y u = −|x|2α u n−2 , where x ∈ R 2 , y ∈ Rn−2 , n ≥ 3 and α > 0. We classify positive solutions with second order derivatives satisfying a suitable growth near the set x = 0.
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