报告题目：Solutions for conformally invariant fractional Laplacian equations with multi-bumps centered in lattices
报 告 人：唐仲伟 教授（北京
报告时间：2019年6月6日(周四) 9:00-10:00
报告地点：磬苑校区数学科学学院H306
报告摘要：In this talk, we consider the following nonlinear elliptic equation involving the fractional Laplacian with critical exponent:
$$(-\Delta)^{s}u=K(x)u^{\frac{N+2s}{N-2s}}, u>0 \textmd{in}{\Bbb R}^{N},$$ where $s\in (0,1)$ and $N>2+2s,$ $K>0$ is periodic in $(x_{1},\ldots, x_{k})$ with $1\leq k<\frac{N-2s}{2}$. Under some natural conditions on $K$ near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in ${\Bbb R}^{k},$ including infinite lattices. On the other hand, to obtain positive solution with infinite bumps such that the bumps locate in lattices in ${\Bbb R}^{k},$ the restriction on $1\leq k<\frac{N-2s}{2}$ is in some sense optimal, since we can show that for $ k\geq\frac{N-2s}{2},$ no such solutions exist. This is a joint work with Dr. Miaomiao Niu and Dr.Lushun Wang.
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科学技术处
2019年6月3日