A Class of Prescribed Weingarten Curvature Equations for Locally Convex Hypersurfaces with Boundary in Rn+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{n+1}$$\end{document}

In this paper, we consider a class of prescribed Weingarten curvature equations for strictly locally convex hypersurfaces with boundary in Rn+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{n+1}$$\end{document}. Under some sufficient conditions, we obtain an existence result using a two-step continuity process based on the a priori estimates for solutions to prescribed Weingarten curvature equations.