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 u = a(x)f (u) + μb(x)|∇u| q , x ∈ R N (N ≥ 3), where μ > 0, q > 0 and a, b ∈ C α loc (R N) (α ∈ (0, 1)). The weight a is nonnegative, b is able to change sign in R N , and f ∈ C 1 [0, ∞) is positive and nondecreasing on (0, ∞) and rapidly or regularly varying at infinity. Additionally, we investigate the uniqueness of entire large solutions.