| Abstract: |
| In this talk, we consider two properties of positive weak solutions of quasilinear elliptic equations, $-\Delta_{m}u=u^q|\nabla u|^p\ \mathrm{in}\ \mathbb{R}^N$, with nonlinear gradient terms. First, we show a Liouville-type theorem for positive weak solutions of the equation involving the $m$-Laplacian operator. The technique of Bernstein gradient estimates is ultilized to study the case $p |
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