@Article{JPDE-35-4,
author = {Xiaotao, Qian},
title = {Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three},
journal = {Journal of Partial Differential Equations},
year = {2022},
volume = {35},
number = {4},
pages = {382--394},
abstract = {<p style="text-align: justify;">In this paper, we are interested in the following nonlocal problem with critical exponent \begin{align*} \begin{cases} -\left(a-b\displaystyle\int_{\Omega}|\nabla u|^2{\rm d}x\right)\Delta u=\lambda |u|^{p-2}u+|u|^{4}u, &amp;\quad x\in\Omega,\\ u=0,&nbsp; &amp;\quad x\in\partial\Omega, \end{cases} \end{align*} where $a,b$ are positive constants, $2&lt;p&lt;6$, $\Omega$ is a smooth bounded domain in $\mathbb{R}^3$ and $\lambda&gt;0$ is a parameter. By variational methods, we prove that problem has a positive ground state solution $u_b$ for $\lambda&gt;0$ sufficiently large. Moreover, we take $b$ as a parameter and study the asymptotic behavior of $u_b$ when $b\searrow0$.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v35.n4.6},
url = {https://global-sci.com/article/88123/positive-ground-state-solutions-for-a-critical-nonlocal-problem-in-dimension-three}
}