| Abstract: |
| Here we consider the nonnegative solutions of equations in a punctured ball
$B(0,R)\setminus\left\{ 0\right\} \subset\mathbb{R}^{N}$ or in $\mathbb{R}^{N}$, of the type
$$
-\Delta u=u^{p}|\nabla u|^{q}
$$
where $p+q>1$. We give new a priori estimates on the solutions and their gradient, and Liouville type results, extending the case $q=0$ of the well known Emden-Fowler equation. We use Bernstein technique and Osserman`s or Gidas-Spruck`s type methods. The most interesting case corresponds to $q |
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