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- W4311946178 abstract "We consider the Hardy-H'enon system $-Delta u =|x|^a v^p$, $-Delta v =|x|^b u^q$ with $p,q>0$ and $a,bin {mathbb R}$ and we are concerned in particular with the Liouville property, i.e. the nonexistence of positive solutions in the whole space ${mathbb R}^N$. In view of known results, it is a natural conjecture that this property should be true if and only if $(N+a)/(p+1)+$ $(N+b)/(q+1)>N-2$. In this paper, we prove the conjecture for dimension N=3 in the case of bounded solutions and in dimensions $Nle 4$ when $a,ble 0$, among other partial nonexistence results. As far as we know, this is the first optimal Liouville type result for the Hardy-H'enon system. Next, as applications, we give results on singularity and decay estimates as well as a priori bounds of positive solutions." @default.
- W4311946178 created "2023-01-03" @default.
- W4311946178 creator A5081260461 @default.
- W4311946178 date "2011-08-05" @default.
- W4311946178 modified "2023-10-18" @default.
- W4311946178 title "Liouville-type theorems and bounds of solutions for Hardy-H'enon elliptic systems" @default.
- W4311946178 doi "https://doi.org/10.48550/arxiv.1108.1312" @default.
- W4311946178 hasPublicationYear "2011" @default.
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