Existence and Asymptotics of Normalized Ground States for a Sobolev Critical Kirchhoff Equation

In the present paper, we investigate the existence and asymptotic properties of normalized solutions for the following Kirchhoff-type equation with Sobolev critical growth [graphic not available: see fulltext] where a,b,m,μ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a, \ b, \ m, \ \mu >0$$\end{document} and 143<p<6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{14}{3}<p<6$$\end{document}. With the aid of the Sobolev subcritical approximation method that is the first time used to consider mass constrained Kirchhoff-type problems, and Schwartz symmetrization rearrangements, we obtain the existence of normalized ground states. Moreover, the asymptotic behavior of these solutions is also studied.