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arXiv · 1806.08510

Nondegeneracy of positive solutions to a Kirchhoff problem with critical Sobolev growth

Gongbao Li·Chang-Lin Xiang
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Abstract

In this paper, we prove uniqueness and nondegeneracy of positive solutions to the following Kirchhoff equations with critical growth \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\Delta u=u^{5}, & u>0 & \text{in }\mathbb{R}^{3},\end{eqnarray*} where $a,b>0$ are positive constants. This result has potential applications in singular perturbation problems concerning Kirchhoff equaitons.

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Gongbao Li, Chang-Lin Xiang. 2018-06-22. Nondegeneracy of positive solutions to a Kirchhoff problem with critical Sobolev growth. https://arxiv.org/abs/1806.08510

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