Liouville theorem for quasilinear elliptic equations in ${\mathbb{R}}^N$

We prove Liouville theorem for the equation ${\mathrm{\Delta }}_{m}v+v^p+M\mathrm{\mid }\mathrm{\nabla }v{\mathrm{\mid }}^q=0$ in a domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$, with $M\in \mathbb{R}$ in the critical and subcritical case. As a natural extension of our recent work \cite{MWZ}, the proof is based on an integral identity and Young’s inequality.