Liouville-type theorem for stable solutions of the Kirchhoff equation with negative exponent
Received:July 04, 2019  Revised:November 28, 2019
Key Word: Kirchhoff equation   Negative exponent   Stable solution   Nonexistence.  
Fund ProjectL:Supported by the National Natural Science Foundation of China(Grant No. 11571092); Jiangsu Province Natural Science Research Projects in Colleges and Universities(19KJD100002); the Natural Science Foundation of Shandong Province(Grant No. ZR2018MA017) and the China Postdoctoral Science Foundation (Grant No. 2017M610436).
Author NameAffiliationE-mail
Yunfeng Wei School of Statistics and Mathematics, Nanjing Audit University 
Caisheng Chen College of Science, Hohai University  
Hongwei Yang College of Mathematics and Systems Science, Shandong University of Science and Technology  
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      In this paper, we are concerned with Liouville-type theorem for stable solutions of the Kirchhoff equation $$ \align M(\int_{\mathbb{R}^N}|\nabla u|^2dx)\Delta u=&g(x)u^{-q}, x\in \mathbb{R}^N,\tag 0.1 \endalign $$ where $M(t)=a+bt^{\theta}, a>0, b, \theta\ge0, \theta=0$ if and only if $b=0$. $N\geq2, q>0$ and the nonnegative function $g(x)\in L^{1}_{loc}(\mathbb{R}^N)$. Under suitable conditions on $g(x), \theta$ and $q$, the nonexistence of positive stable solution to equation (0.1) is investigated.
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