@article{Qin2025, 
author = {Chun Qin and Jie Yang},
title = {Normalized solutions to lower critical Choquard equation with mixed local-nonlocal operators},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {28668-28688},
keywords = {local and nonlocal operators, Choquard equation, normalized ground state, HLS lower critical exponent},
url = {https://www.sciopen.com/article/10.3934/math.20251262},
doi = {10.3934/math.20251262},
abstract = {This paper investigates the existence and non-existence of normalized ground state solutions for the following Choquard equation with mixed local and nonlocal operators, involving the Hardy-Littlewood-Sobolev (HLS) lower critical exponent. For the critical case    p  =  2  +      4    N  , we employ fibering map analysis to establish the non-existence of solutions. In the subcritical regime    2  <  p  <  2  +      4    N  , we utilize variational methods to prove the existence of normalized ground states, which are shown to be radially symmetric and strictly decreasing in        |    x      |  . For the supercritical case    2  +      4    N    <  p  <      2    s    ∗  , we introduce a homotopy-stable family to construct a Palais–Smale sequence with a negative Lagrange multiplier. By analyzing the compactness properties of this sequence, we demonstrate the existence of normalized ground state solutions in this regime as well.}
}