Infinitely many singularities and denumerably many positive solutions for a second-order impulsive Neumann boundary value problem

Using a fixed point theorem of cone expansion and compression of norm type and a new method to deal with the impulsive term, we prove that the second-order singular impulsive Neumann boundary value problem has denumerably many positive solutions. Noticing that M>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M>0$\end{document}, our main results improve many previous results.