Normalized ground states for fractional energy critical Kirchhoff equations with the mass critical and supercritical perturbations

We study the existence and asymptotic behavior of normalized ground states for the nonlinear fractional energy critical Kirchhoff equation with mass critical and supercritical perturbations in RN(N=2,3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>N(N=2,3)$$\end{document}. The presence of the fractional energy critical exponent in the Kirchhoff nonlocal setting makes the problem more challenging, as the underlying fractional order algebraic equation cannot be solved precisely. To address this challenge, we establish the threshold energy estimates based on the monotonicity trick and truncation technique. By combining the minimax procedure and Poho & zcaron;aev manifold decomposition, we prove the existence of the normalized ground states. Moreover, we also explore the asymptotic behavior of the normalized ground states.