Singular elliptic problems: existence, non-existence and boundary behavior
type: Item
instance of: scholarly article
title: Singular elliptic problems: existence, non-existence and boundary behavior
zbMATH Open document ID: 1162.35030
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-04-19T00:00:00Z
review text: The authors study the existence, uniqueness and boundary behaviour of solutions of the (possibly) singular semilinear elliptic problem \[ -\Delta u= \rho a(x) g(u)+ \lambda b(x) f(u)\quad\text{in }\Omega, \] \[ u> 0\quad\text{in }\Omega,\qquad u= 0\quad\text{on }\partial\Omega, \] where \(\Omega\subset\mathbb{R}^d\) is a bounded domain with smooth boundary \(\partial\Omega\), \(p\), \(\lambda\geq 0\), \(a,b:\overline\Omega\to [0,\infty)\) are Hölder continuous with exponent \(\nu\in (0,1)\). The main feature here is that \(g(t)\), \(f(t)\to \infty\) as \(t\to 0\) (at least one of them). To this end the authors use a variational method.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5144876
zbMATH Keywords: semilinear singular elliptic equations
zbMATH Keywords: boundary behavior
zbMATH Keywords: variational methods
author: José Valdo A. Gonçalves
author: Carlos A. Santos
MaRDI profile type: Publication
full work available at URL: j.na.2006.03.003
OpenAlex ID: W2029930959
cites work: Q3269389
cites work: Remarks on sublinear elliptic equations
cites work: On a dirichlet problem with a singular nonlinearity
cites work: Combined effects of asymptotically linear and singular nonlinearities in bifurcation problems of Lane-Emden-Fowler type
cites work: On a singular nonlinear dirichlet problem
cites work: Q4810597
cites work: Q3803507
cites work: On a class of sublinear singular elliptic problems with convection term
cites work: Sublinear singular elliptic problems with two parameters.
cites work: Multi-parameter bifurcation and asymptotics for the singular Lane–Emden–Fowler equation with a convection term
cites work: Q5187597
cites work: Regularity of an elliptic problem with a singular nonlinearity
cites work: Classical and weak solutions of a singular semilinear elliptic problem
cites work: On singular boundary value problems for the Monge-Ampère operator
cites work: On a Singular Nonlinear Elliptic Boundary-Value Problem
cites work: Multiple positive solutions of singular elliptic problems.
cites work: On a singular nonlinear semilinear elliptic problem
cites work: Iterative solution for a singular nonlinear elliptic problem
cites work: Combined effects of singular and superlinear nonlinearities in some singular boundary value problems.
cites work: A nonlinear singular boundary value problem
cites work: Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems
cites work: Critical points and positive solutions of singular elliptic boundary value problems
cites work: Positive solution of a singular nonlinear elliptic boundary value problem.
DOI: 10.1016/J.NA.2006.03.003
Recommended article: Q5741116
Recommended article: Q3202539
Recommended article: Q4899497
Recommended article: Existence and nonexistence results for classes of singular elliptic problem
Recommended article: Q4702042
Recommended article: Existence and nonexistence of solutions for a singular elliptic problem with a nonlinear boundary condition
Recommended article: Q4520076
Recommended article: Boundary value problems for singular elliptic equations
Recommended article: Existence and estimates of solutions for singular nonlinear elliptic problems
Recommended article: Existence results for singular elliptic equations
description: scientific article; zbMATH DE number 5144876