Gongbao Li, Chang-Lin Xiang
Published 2018-06-22Version 1
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.
Positive solutions for a Kirchhoff problem of Brezis-Nirenberg type in dimension four
Uniqueness and nondegeneracy of positive solutions of $\Ds u+u=u^p$ in $\R^N$ when $s$ is close to 1
Infinitely many positive solutions for nonlinear equations with non-symmetric potential
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