Solutions stable outside a compact set for anisotropic quasilinear equations with negative exponent or exponential nonlinearity

Nhat Vy Huynh, Phuong Le

We study the equations ${\Delta }_p^{H}u=u^{-q}$, $u>0$, and $-{\Delta }_p^{H}u=e^u$ in ${\mathbb{R}}^N$, where ${\Delta }_p^{H}u=\mathrm{div}(H(\nabla u{)}^{p-1}\nabla H(\nabla u))$ is the Finsler $p$-Lap…