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On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation by Gao, Fashun; Yang, Minbo is a scholarly article available to read on EtoBox.

What is On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation about?

We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation $$-\Delta u =\left(\int_{\Omega}\frac{|u|^{2_{\mu}^{\ast}}}{|x-y|^{\mu}}dy\right)|u|^{2_{\mu}^{\ast}-2}u+\lambda u\4.14mm\mbox{in}\1.14mm \Omega, $$ where $\Omega$ is a bounded domain of $\mathbb{R}^N$, with Lipschitz boundary, $\lambda$ is a real parameter, $N\geq3$, $2_{\mu}^{\ast}=(2N-\mu)/(N-2)$ is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.

Author

Gao, Fashun; Yang, Minbo

Published

2016

Language

EN