| Abstract: |
| In this talk, I will present our recent results in constructing multi-bump solutions for the critical Choquard equation. These solutions are obtained by combining the variational gluing method with a penalization technique. In contrast to the local Yamabe equation, we find that for all dimensions $N\geq 3$, there are infinitely many $\ell$-bump ($\ell\geq2$) positive solutions with polynomial decay. This occurs when the potential function displays periodicity in one variable and features a global maximum with a rapid decay rate in the vicinity of that maximum point. This talk is based on the joint work with Professor Xu Zhang from Central South University, China. |
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