Wei Wei

Liouville theorem for a class of p-Laplace type equations on manifolds

We study a class of $p$-Laplace equations $$\Delta_p u-\lambda u^{p-1}+ u^{q-1}=0$$ on a closed $n$-dimensional Riemannian manifold $(M,g)$ with $\operatorname{Ric}\geqslant(n-1)g$. For $1<p<2$, $p<q<p^*$, and $0<\lambda<S_{p,q}^{-1}$, where $$S_{p,q}=\frac{q-p}{2}(\frac p n)^{\frac p 2}\Big(\frac{(p^*-1)^2(2-p)}{(p_*-...