@article{Sun2024, 
author = {Xizheng Sun and Zhiqing Han},
title = {Note on normalized solutions to a kind of fractional Schrödinger equation with a critical nonlinearity},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {21641-21655},
keywords = {nonlinear fractional Schrödinger equation, normalized solutions, critical nonlinearity},
url = {https://www.sciopen.com/article/10.3934/math.20241052},
doi = {10.3934/math.20241052},
abstract = {In this paper, we study normalized solutions of the fractional Schrödinger equation with a critical nonlinearity   {(−Δ)su=λu+|u|p−2u+|u|2s∗−2u,x∈RN,∫RNu2dx=a2,u∈Hs(RN),where  N≥2,  s∈(0,1),  a>0,  2<p<2s∗≜2NN−2s and  (−Δ)s is the fractional Laplace operator. In the purely  L2-subcritical perturbation case  2<p<2+4sN, we prove the existence of a second normalized solution under some conditions on  a,  p,  s, and  N. This is a continuation of our previous work (Z. Angew. Math. Phys., 73 (2022) 149) where only one solution is obtained.}
}