Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term

Abstract

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.

Keywords

• Blow-up rates
• Entire large solutions
• Convection term