Positive solution of a singular nonlinear elliptic boundary value problem.
type: Item
instance of: scholarly article
title: Positive solution of a singular nonlinear elliptic boundary value problem.
zbMATH Open document ID: 1145.35375
DOI: 10.1016/S0096-3003(02)00922-0
author: Miaoxin Yao
author: Jian-Xun Zhao
published in: Applied Mathematics and Computation
publication date: 2004-01-26T00:00:00Z
review text: The authors consider the following singular elliptic problem \[ \begin{cases} \Delta u+ g(x) u^\alpha+ h(x) u^{-\beta}= 0\quad &\text{in }\Omega,\\ u> 0\quad &\text{in }\Omega,\\ u= 0\quad &\text{on }\partial\Omega,\end{cases}\tag{1} \] where \(\alpha\in (0,1)\), \(\beta> 0\), \(\Omega\) is a bounded domain in \(\mathbb R^N\) with smooth boundary. Using super- and subsolution argument together with a monotonic approaching, the authors establish two theorems regarding, respectively the existence and the uniqueness of solutions for (1), in which the restriction on constant \(\beta\) and the functions \(g\) and \(h\) are relaxed in some sense.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 2032664
zbMATH Keywords: positive solution
zbMATH Keywords: nonlinear elliptic boundary value problem
zbMATH Keywords: super- and subsolution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q5627113
cites work: Q5531285
cites work: A Nonlinear Singular Boundary Value Problem in the Theory of Pseudoplastic Fluids
cites work: On a dirichlet problem with a singular nonlinearity
cites work: An elliptic equation with singular nonlinearity
cites work: Q3276827
cites work: Q5187597
cites work: Q3710895
cites work: On a Singular Nonlinear Elliptic Boundary-Value Problem
cites work: A remark on the preceding paper of Amann
cites work: Existence and approximation of solutions of non-linear elliptic equations
cites work: Iterative solution for a singular nonlinear elliptic problem
cites work: On a singular nonlinear semilinear elliptic problem
cites work: A degenerate diffusion equation with a nonlinear source term
description: scientific article; zbMATH DE number 2032664