Multiple positive solutions for second order one dimensional p-Laplacian boundary value problems

The aim of this article is to study the boundary value problems of second order ordinary differential equations with p-Laplacian operators under Riemann-Stieltjes integral boundary conditions. First, by applying the invertibility of operator Phi p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Phi _{p}$$\end{document} and iterative methods, we transform the existence of positive solutions of the problems into the number of fixed points of the corresponding integral equations. Second, by utilizing the Gronwall-type inequality and integral factor methods, we get a priori bounds for norms of derivatives and allow the nonlinearity to be p-th growth with respect to the derivative. Finally, by using the existence property of fixed point index, we obtain the existence of multiple positive solutions of the problems, and illustrate our conclusions through two examples.