Fractional Choquard equation with critical nonlinearities
Fractional Choquard equation with critical nonlinearities
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DOI：
10.1007/s00030-017-0487-1
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发表时间：
2016-05
期刊：
影响因子：
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通讯作者：
T. Mukherjee;K. Sreenadh
中科院分区：
文献类型：
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作者：
T. Mukherjee;K. Sreenadh
本文研究了具有分数阶Laplacian \[（-\De）^s u = \left（\int_{\Om}\frac{|u| ^{2^*_{\mu，s}}}{|X-Y| ^{\mu}}\mathrm{d}y \right）|u| ^{2^*_{\mu，s}-2}u +\la u \; \text{in } \Om，\]其中$\Om $是中具有Lipschitz边界的有界区域，$\la $是一个真实的参数，是Hardy-Littlewood-Sobolev不等式意义下的临界指数.利用变分方法得到了上述方程解的存在性、多解性、正则性和不存在性结果。
In this article, we study the Brezis-Nirenberg type problem of nonlinear Choquard equation involving a fractional Laplacian \[ (-\De)^s u = \left( \int_{\Om}\frac{|u|^{2^*_{\mu,s}}}{|x-y|^{\mu}}\mathrm{d}y \right)|u|^{2^*_{\mu,s}-2}u +\la u \; \text{in } \Om,\] where $\Om $ is a bounded domain inwith Lipschitz boundary, $\la $ is a real parameter,,andis the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. We obtain some existence, multiplicity, regularity and nonexistence results for solution of the above equation using variational methods.