@article{Qiu2024, 
author = {Xin Qiu and Zeng Qi Ou and Ying Lv},
title = {Normalized solutions to nonautonomous Kirchhoff equation},
year = {2024},
journal = {Communications in Analysis and Mechanics},
volume = {16},
number = {3},
pages = {457-486},
keywords = {nonautonomous Kirchhoff equations, normalized solutions, bound state solution, L2-critical exponent},
url = {https://www.sciopen.com/article/10.3934/cam.2024022},
doi = {10.3934/cam.2024022},
abstract = {In this paper, we studied the existence of normalized solutions to the following Kirchhoff equation with a perturbation:   {−(a+b∫RN|∇u|2dx)Δu+λu=|u|p−2u+h(x)|u|q−2u,inRN,∫RN|u|2dx=c,u∈H1(RN),where  1≤N≤3,a,b,c>0,1≤q<2,  λ∈R. We treated three cases:(i) When  2<p<2+4N,h(x)≥0, we obtained the existence of a global constraint minimizer.(ii) When  2+8N<p<2∗,h(x)≥0, we proved the existence of a mountain pass solution.(iii) When  2+8N<p<2∗,h(x)≤0, we established the existence of a bound state solution.}
}