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The Existence of a Nontrivial Weak Solution to a Double Critical Problem Involving a Fractional Laplacian in ℝN with a Hardy Term
Acta Mathematica Scientia ( IF 1 ) Pub Date : 2020-10-10 , DOI: 10.1007/s10473-020-0613-8 Gongbao Li , Tao Yang
Acta Mathematica Scientia ( IF 1 ) Pub Date : 2020-10-10 , DOI: 10.1007/s10473-020-0613-8 Gongbao Li , Tao Yang
In this paper, we consider the existence of nontrivial weak solutions to a double critical problem involving fractional Laplacian with a Hardy term: \begin{equation} \label{eq0.1} (-\Delta)^{s}u-{\gamma} {\frac{u}{|x|^{2s}}}= {\frac{{|u|}^{ {2^{*}_{s}}(\beta)-2}u}{|x|^{\beta}}}+ \big [ I_{\mu}* F_{\alpha}(\cdot,u) \big](x)f_{\alpha}(x,u), \ \ u \in {\dot{H}}^s(\R^{n}) \end{equation} where $s \in(0,1)$, $0\leq \alpha,\beta<2s
中文翻译:
对包含哈代项ℝN 中的分数拉普拉斯算子的双重临界问题的非平凡弱解的存在性
在本文中,我们考虑了一个包含哈代项的分数拉普拉斯算子的双重临界问题的非平凡弱解的存在:\begin{equation} \label{eq0.1} (-\Delta)^{s}u-{\ gamma} {\frac{u}{|x|^{2s}}}= {\frac{{|u|}^{ {2^{*}_{s}}(\beta)-2}u} {|x|^{\beta}}}+ \big [ I_{\mu}* F_{\alpha}(\cdot,u) \big](x)f_{\alpha}(x,u), \ \ u \in {\dot{H}}^s(\R^{n}) \end{equation} where $s \in(0,1)$, $0\leq \alpha,\beta<2s
更新日期:2020-10-10
中文翻译:
对包含哈代项ℝN 中的分数拉普拉斯算子的双重临界问题的非平凡弱解的存在性
在本文中,我们考虑了一个包含哈代项的分数拉普拉斯算子的双重临界问题的非平凡弱解的存在:\begin{equation} \label{eq0.1} (-\Delta)^{s}u-{\ gamma} {\frac{u}{|x|^{2s}}}= {\frac{{|u|}^{ {2^{*}_{s}}(\beta)-2}u} {|x|^{\beta}}}+ \big [ I_{\mu}* F_{\alpha}(\cdot,u) \big](x)f_{\alpha}(x,u), \ \ u \in {\dot{H}}^s(\R^{n}) \end{equation} where $s \in(0,1)$, $0\leq \alpha,\beta<2s