Multiplicity of positive solutions for fractional elliptic systems involving sign-changing weight

In this paper, we study the multiplicity results of positive solutions for a fractional elliptic system involving both concave-convex and critical growth terms. With the help of Morse theory and the Ljusternik-Schnirelmann category, we investigate how the coefficient h(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$h(x)$\end{document} of the critical nonlinearity affects the number of positive solutions of that problem and we get some results as regards the relationship between the number of positive solutions and the topology of the global maximum set of h.