• Corpus ID: 221139999

Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms

  title={Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms},
  author={Caihong Chang and Bei Hu and Zhengce Zhang},
  journal={arXiv: Analysis of PDEs},
This paper is concerned with two properties of positive weak solutions of quasilinear elliptic equations with nonlinear gradient terms. First, we show the Liouville-type theorems for positive weak solutions of the equation involving the $m$-Laplacian operator \begin{equation*} -\Delta_{m}u=u^q|\nabla u|^p\ \ \ \mathrm{in}\ \mathbb{R}^N, \end{equation*} where $N\geq1$, $m>1$ and $p,q\geq0$. This paper mainly adopts the technique of Bernstein gradient estimates to study from two cases: $p=m$ and… 
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