Critical growth fractional elliptic systems with exponential nonlinearity

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• 作者：J. Giacomoni^a ; ^{jacques.giacomoni@univ-pau.fr" class="auth_mail" title="E-mail the corresponding author} ; Pawan Kumar Mishra^b ; ^{pawanmishra31284@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; K. Sreenadh^b ; ^{sreenadh@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fractional elliptic systems ; Exponential nonlinearity ; Trudinger&ndash ; Moser inequality
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：136
• 期：Complete
• 页码：117-135
• 全文大小：663 K

文摘

We study the existence of positive solutions for the system of fractional elliptic equations of the type, where 1<p+q<2$1<p+q<2$, 22ed9eba55" title="Click to view the MathML source">h₁(u,v)=(α+2u²)∣u∣^α−2u∣v∣^β,h₂(u,v)=(β+2v²)∣u∣^α∣v∣^β−2v$h_1(u,v)=(\alpha +2u^2)\mid u{\mid }^{\alpha -2}u\mid v{\mid }^{\beta },h_2(u,v)=(\beta +2v^2)\mid u{\mid }^{\alpha }\mid v{\mid }^{\beta -2}v$ and α+β>2$\alpha +\beta >2$. Here ${(-\Delta )}^{\frac{1}{2}}$ is the fractional Laplacian operator. We show the existence of multiple solutions for suitable range of λ$\lambda$ by analyzing the fibering maps and the corresponding Nehari manifold. We also study the existence of positive solutions for a superlinear system with critical growth exponential nonlinearity.