Boundary blow-up solutions and their applications in quasilinear elliptic equations
type: Item
instance of: scholarly article
title: Boundary blow-up solutions and their applications in quasilinear elliptic equations
zbMATH Open document ID: 1162.35028
DOI: 10.1007/BF02893084
author: Yihong Du
author: Zongming Guo
published in: Journal d'Analyse Mathématique
publication date: 2003-10-27T00:00:00Z
review text: It is considered the quasilinear elliptic equation \[ -\Delta_p u=a| u| ^{p-2}u-b(x)| u| ^{q-1}u\quad\text{ in}\;\Omega,\quad u=0\;\text{ on}\;\partial\Omega, \] where \(\Delta_pu=\text{ div\,}(| Du| ^{p-2}Du),\) \(1<p<\infty,\) \(q>p-1,\) \(a\) is a real parameter, \(b(x)\geq 0\) is in \(C^\mu(\bar\Omega)\) \((1>\mu>0),\) and \(\Omega\) is a bounded smooth domain in \({\mathbb R}^N\) \((N\geq 2).\) It is also considered the problem \[ -\Delta_p u=a| u| ^{p-2}u-b| u| ^{q-1}u\quad\text{ in}\;{\mathbb R}^N, \] where \(b>0\) is a constant. Based on a comparison principle it is studied the existence, uniqueness and asymptotic behavior of various boundary blow-up solutions.
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1997291
zbMATH Keywords: quasilinear elliptic equations
zbMATH Keywords: blow-up solutions
zbMATH Keywords: comparison principle
reviewed by: Lubomira Softova
MaRDI profile type: Publication
cites work: On the solvability of a semilinear elliptic equation via an associated eigenvalue problem
cites work: Branches of positive solutions for some semilinear Schrödinger equations
cites work: `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
cites work: Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary
cites work: On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations
cites work: Existence of positive solutions for some problems with nonlinear diffusion
cites work: Positive solutions of a semilinear elliptic equation on a compact manifold
cites work: Explosive solutions of quasilinear elliptic equations: existence and uniqueness
cites work: Q3726641
cites work: Q4857890
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: Some existence and multiplicity results for a class of quasilinear elliptic eigenvalue problems
cites work: Uniqueness and Flat Core of Positive Solutions for Quasilinear Elliptic Eigenvalue Problems in General Smooth Domains
cites work: Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large
cites work: Large and small solutions of a class of quasilinear elliptic eigenvalue problems
cites work: Q3998030
cites work: Rearrangements and convexity of level sets in PDE
cites work: On a familiy of torsional creep problems.
cites work: On solutions of δu=f(u)
cites work: On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
cites work: Linear and quasilinear elliptic equations
cites work: Quasilinear elliptic equations with boundary blow-up
cites work: Stationary profiles of degenerate problems when a parameter is large
cites work: Q3141808
cites work: Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations
cites work: On the Positive Solutions of Semilinear Equations Δu + λu - hu p = 0 on the Compact Manifolds
cites work: On the inequality \(\Delta u \geqq f (u)\)
cites work: Q4093139
cites work: Diffusion of Fluid in a Fissured Medium with Microstructure
cites work: Positive solutions of a degenerate elliptic equation with logistic reaction
cites work: On The Dirichletproblem for Quasilinear Equations
cites work: Regularity for a more general class of quasilinear equations
cites work: A strong maximum principle for some quasilinear elliptic equations
full work available at URL: https://doi.org/10.1007/bf02893084
OpenAlex ID: W1989914132
description: scientific article; zbMATH DE number 1997291