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arXiv · 1804.08084

Coron problem for nonlocal equations invloving Choquard nonlinearity

Divya Goel·Vicentiu D. Radulescu·K. Sreenadh
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Abstract

We study the problem \[ -\De u = \left(\int_{\Om}\frac{|u(y)|^{2^*_μ}}{|x-y|^μ}dy\right)|u|^{2^*_μ-2}u, \; \text{in}\; \Om,\quad u = 0 \; \text{ on } \pa \Om , \] where $\Om$ is a smooth bounded domain in $\mathbb{R}^N( N\geq 3)$, $2^*_μ=\frac{2N-μ}{N-2}$. we prove the existence of a positive solution of the above problem in an annular type domain when the inner hole is sufficiently small.

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Divya Goel, Vicentiu D. Radulescu, K. Sreenadh. 2019-05-17. Coron problem for nonlocal equations invloving Choquard nonlinearity. https://arxiv.org/abs/1804.08084

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