Nondegeneracy and uniqueness for boundary blow-up elliptic problems
type: Item
instance of: scholarly article
title: Nondegeneracy and uniqueness for boundary blow-up elliptic problems
zbMATH Open document ID: 1170.35405
published in: Journal of Differential Equations
publication date: 2006-04-28T00:00:00Z
review text: The aim of the author is to show uniqueness for \[ \Delta u=\lambda a(x) u^p+ g(x,u)\quad\text{in }\Omega, \] \[ u=+\infty\quad\text{on }\partial\Omega, \] where \(p> 1\), \(a(x)\) is a continuous function which can be singular near \(\partial\Omega\), \(g(x,u)\) is a prescribed continuous function and \(\Omega\) is a smooth bounded domain in \(\mathbb R^N\). The author determines asymptotic behaviour this unique solution for large enough \(\lambda\). The author considers more general problem, obtained by replacing \(u^p\) by \(e^u\) or ``logistic type'' function \(f(u)\). The main tool of the author is the implicit function theorem.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 5019771
zbMATH Keywords: Boundary blow-up problems
zbMATH Keywords: Nondegeneracy
zbMATH Keywords: Implicit function theorem
author: Jorge García-Melian
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jde.2005.05.001
OpenAlex ID: W2066531603
cites work: Multiple boundary blow-up solutions for nonlinear elliptic equations
cites work: Localization on the Boundary of Blow-up for Reaction–Diffusion Equations with Nonlinear Boundary Conditions
cites work: Q4312129
cites work: Q3349992
cites work: `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
cites work: On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems.
cites work: On an elliptic problem with boundary blow-up and a singular weight: the radial case
cites work: Uniqueness and boundary behavior of large solutions to elliptic problems with singular weights
cites work: Effects of Certain Degeneracies in the Predator-Prey Model
cites work: The influence of domain geometry in boundary blow-up elliptic problems.
cites work: Explosive solutions of quasilinear elliptic equations: existence and uniqueness
cites work: Effects of a degeneracy in the competition model. I: Classical and generalized steady-state solutions
cites work: Effects of a degeneracy in the competition model. II: Perturbation and dynamical behaviour
cites work: Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations
cites work: LOGISTIC TYPE EQUATIONS ON ℝN BY A SQUEEZING METHOD INVOLVING BOUNDARY BLOW-UP SOLUTIONS
cites work: Q4444851
cites work: Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs
cites work: Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up
cites work: The solvability of an elliptic system under a singular boundary condition
cites work: Boundary blow-up solutions to elliptic systems of competitive type
cites work: Q4454333
cites work: Q4040640
cites work: Q3233048
cites work: On solutions of δu=f(u)
cites work: Q3487854
cites work: On a problem of Bieberbach and Rademacher
cites work: Asymptotic behavior of solutions of boundary blow-up problems
cites work: Q4052566
cites work: Q4458816
cites work: Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations
cites work: Large solutions to some non-linear O.D.E. with singular coefficients.
cites work: On the inequality \(\Delta u \geqq f (u)\)
cites work: Semilinear elliptic equations with uniform blow-up on the boundary
cites work: A remark on the existence of explosive solutions for a class of semilinear elliptic equations
DOI: 10.1016/J.JDE.2005.05.001
description: scientific article