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...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
SpringerOpen
2018-12-01
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Series: | Boundary Value Problems |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1186/s13661-018-1101-0 |
Summary: | 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. |
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ISSN: | 1687-2770 |