On the number of positive solutions for a four-point boundary value problem with generalized Laplacian

This paper mainly deals with a four-point boundary value problem for a class of generalized Laplacian equations with singular weight and positive parameter. By applying the fixed point theorem of expansion/compression of a cone and Schauder’s fixed point theorem, we obtain the relations between the number of positive solutions and two different kinds of asymptotic behaviors of the nonlinearity at 0 and ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\infty $$\end{document}. The conclusions in this paper can also be suitable for the corresponding multi-point boundary value problem.