Liouville type theorems for stable solutions of the weighted elliptic system

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• 作者：Liang-Gen Hu^a ; ^{hulianggen@tom.com" class="auth_mail" title="E-mail the corresponding author} ; Jing Zeng^b ; ^{zengjing@fjnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Weighted elliptic system ; Stable solutions ; Liouville type theorem ; Iteration
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：437
• 期：2
• 页码：882-901
• 全文大小：399 K

文摘

We examine the weighted elliptic system and prove Liouville type theorems for the classical positive and nonnegative stable solutions in higher dimension. In particular, there are no positive stable solutions for any N≤12+5α$N\le 12+5\alpha$, p>1$p>1$ and α>0$\alpha >0$. Our proof is based on a combination of the bootstrap argument, Souplet's inequality and intermediate stability criterion, which is used to obtain sharp results.