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Article overview
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Uniqueness and nondegeneracy of sign-changing radial solutions to an almost critical elliptic problem | | Weiwei Ao
; Juncheng Wei
; Wei Yao
; | | Date: |
15 Oct 2015 | | Abstract: | We study sign-changing radial solutions for the following semi-linear
elliptic equation egin{align*} Delta u-u+|u|^{p-1}u=0quad{
m{in}}
mathbb{R}^N,quad uin H^1(mathbb{R}^N), end{align*} where
$1<p<frac{N+2}{N-2}$, $Ngeq3$. It is well-known that this equation has a
unique positive radial solution and sign-changing radial solutions with exactly
$k$ nodes. In this paper, we show that such sign-changing radial solution is
also unique when $p$ is close to $frac{N+2}{N-2}$. Moreover, those solutions
are non-degenerate, i.e., the kernel of the linearized operator is exactly
$N$-dimensional. | | Source: | arXiv, 1510.4678 | | Services: | Forum | Review | PDF | Favorites | |
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