Coron problem for nonlocal equations invloving Choquard nonlinearity

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 ${\mathbb{R}}^N(N\ge 3)$, $2_{\mu }^{\ast }=\frac{2N-\mu }{N-2}$. we prove the existence of a positive solution of the above problem in an annular type domain when the inner hole is sufficiently small.

26pages

References in corpus (4)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• TOPICAL REVIEW: General relativistic boson stars
• On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation
• Existence of solutions for critical Choquard equations via the concentration compactness method

Cited by in corpus (1)

• Critical growth elliptic problems involving Hardy-Littlewood-Sobolev critical exponent in non-contractible domains