Abstract:

In this paper, we consider the following quasilinear elliptic system

$\begin{eqnarray*}\Delta_{p_i}u_i+\zeta_i (|x|)|\nabla u_i|^{p_i-1}=\eta_i(|x|)f_i (u_1, \cdots, u_m), \;\\mbox{in}\;\ \mathbb{R} ^N, \end{eqnarray*}$

where $i=1, \cdots, m$, $p_i\ge 2$, $\zeta_i$ and $\eta_i$ are positive continuous functions, and $f_i$ is a non-negative continuous function and nondecreasing in each component for every $i\in \{1, 2, \cdots, m\}$. After using some new comparison principle, we are able to show that the system does not admit any nonradial blow-up solutions.

Key words: Quasilinear elliptic system, Comparison principle, Nonexistence, Blow-up solution