On critical systems involving fractional Laplacian

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• 作者：Zhenyu Guo^a ; ^b ; ^{guozy@163.com" class="auth_mail" title="E-mail the corresponding author} ; Senping Luo^b ; ^{luosp1989@163.com" class="auth_mail" title="E-mail the corresponding author} ; Wenming Zou^b ; ^{wzou@math.tsinghua.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Ground state ; Nehari manifold ; Fractional&ndash ; Sobolev critical exponent
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：681-706
• 全文大小：455 K

文摘

Consider the following non-local critical system where (−Δ)^s${(-\mathrm{\Delta })}^s$ is fractional Laplacian, 0<s<1$0<s<1$ and all λ₁,λ₂,μ₁,μ₂,γ>0${\lambda }_1,{\lambda }_2,{\mu }_1,{\mu }_2,\gamma >0$, 2f1444426c8ac06fdeac3f">$2_{⁎}:=\frac{2N}{N-2s}$ is a fractional Sobolev critical exponent, N>2s$N>2s$, f10989532b51f71cd60" title="Click to view the MathML source">α,β>1$\alpha ,\beta >1$, 624225d21dcc252298fa714b5" title="Click to view the MathML source">α+β=2_⁎$\alpha +\beta =2_{⁎}$, and Ω is an open bounded domain in R^N${\mathbb{R}}^N$ with Lipschitz boundary. Under proper conditions, we establish the existence result of the ground state solution to system (0.1).