Existence and Multiplicity Results for Generalized Laplacian Problems with a Parameter

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian equations with a singular weight which may not be integrable. Some existence, multiplicity and nonexistence results of positive solutions under two different 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} are established in terms of different ranges of a parameter. Our approach is based on the fixed point theorem of expansion/compression of a cone and Schauder’s fixed point theorem.