Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term
Abstract In this paper, we analyze the blow-up rates and uniqueness of entire large solutions to the equation Δu=a(x)f(u)+μb(x)|∇u|q $\Delta u=a(x)f(u)+ \mu b(x) |\nabla u|^{q}$, x∈RN $x\in \mathbb{R}^{N}$ ( N≥3 $N\geq 3$), where μ>0 $\mu > 0$, q>0 $q > 0$ and a,b∈Clocα(RN) $a, b\in \mat...
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doaj-6850a7a7253e4ed1a8429871da392aff2020-11-25T00:53:57ZengSpringerOpenBoundary Value Problems1687-27702018-12-012018111410.1186/s13661-018-1101-0Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection termBo Li0Haitao Wan1School of Mathematics and Information Science, Yantai UniversitySchool of Mathematics and Information Science, Shandong Institute of Business and TechnologyAbstract In this paper, we analyze the blow-up rates and uniqueness of entire large solutions to the equation Δu=a(x)f(u)+μb(x)|∇u|q $\Delta u=a(x)f(u)+ \mu b(x) |\nabla u|^{q}$, x∈RN $x\in \mathbb{R}^{N}$ ( N≥3 $N\geq 3$), where μ>0 $\mu > 0$, q>0 $q > 0$ and a,b∈Clocα(RN) $a, b\in \mathrm {C}^{\alpha }_{\mathrm{loc}}(\mathbb{R}^{N})$ ( α∈(0,1) $\alpha \in (0, 1)$). The weight a is nonnegative, b is able to change sign in RN $\mathbb{R}^{N}$, and f∈C1[0,∞) $f\in C^{1}[0, \infty )$ is positive and nondecreasing on (0,∞) $(0, \infty )$ and rapidly or regularly varying at infinity. Additionally, we investigate the uniqueness of entire large solutions.http://link.springer.com/article/10.1186/s13661-018-1101-0Blow-up ratesEntire large solutionsConvection term |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Bo Li Haitao Wan |
spellingShingle |
Bo Li Haitao Wan Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term Boundary Value Problems Blow-up rates Entire large solutions Convection term |
author_facet |
Bo Li Haitao Wan |
author_sort |
Bo Li |
title |
Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term |
title_short |
Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term |
title_full |
Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term |
title_fullStr |
Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term |
title_full_unstemmed |
Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term |
title_sort |
blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term |
publisher |
SpringerOpen |
series |
Boundary Value Problems |
issn |
1687-2770 |
publishDate |
2018-12-01 |
description |
Abstract In this paper, we analyze the blow-up rates and uniqueness of entire large solutions to the equation Δu=a(x)f(u)+μb(x)|∇u|q $\Delta u=a(x)f(u)+ \mu b(x) |\nabla u|^{q}$, x∈RN $x\in \mathbb{R}^{N}$ ( N≥3 $N\geq 3$), where μ>0 $\mu > 0$, q>0 $q > 0$ and a,b∈Clocα(RN) $a, b\in \mathrm {C}^{\alpha }_{\mathrm{loc}}(\mathbb{R}^{N})$ ( α∈(0,1) $\alpha \in (0, 1)$). The weight a is nonnegative, b is able to change sign in RN $\mathbb{R}^{N}$, and f∈C1[0,∞) $f\in C^{1}[0, \infty )$ is positive and nondecreasing on (0,∞) $(0, \infty )$ and rapidly or regularly varying at infinity. Additionally, we investigate the uniqueness of entire large solutions. |
topic |
Blow-up rates Entire large solutions Convection term |
url |
http://link.springer.com/article/10.1186/s13661-018-1101-0 |
work_keys_str_mv |
AT boli blowupratesanduniquenessofentirelargesolutionstoasemilinearellipticequationwithnonlinearconvectionterm AT haitaowan blowupratesanduniquenessofentirelargesolutionstoasemilinearellipticequationwithnonlinearconvectionterm |
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