Multiplicity of normalized solutions to the upper critical fractional Choquard equation with $L^2$-supercritical perturbation
Authors
Yergen Aikyn
Yongpeng Chen
Michael Ruzhansky
Zhipeng Yang
Abstract
We investigate normalized solutions with prescribed $L^2$-norm for the upper critical fractional Choquard equation \[(-Δ)^s u+V(\varepsilon x)u=λu+\big(I_α*|u|^{p}\big)|u|^{p-2}u+\big(I_α*|u|^{q}\big)|u|^{q-2}u\quad\text{in }\mathbb{R}^N,\] where $N>2s$, $00$, the problem admits at least $\mathrm{cat}_{M_δ}(M)$ distinct normalized solutions, where $M$ is the set of global minima of $V$ and these solutions concentrate near $M$ as $\varepsilon\to0$.
