Liouville results for m-Laplace equations of Lane–Emden–Fowler type

We consider sign changing solutions of the equation −Δm(u)=|u|^p−1u$-{\mathrm{\Delta }}_m(u)={|u|}^{p-1}u$ in possibly unbounded domains or in RN${\mathbb{R}}^N$. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The results hold true for m>2$m>2$ and m−1m−1<p<pc(N,m). Here pc(N,m)$p_c(N,m)$ is a new critical exponent, which is infinity in low dimension and is always larger than the classical critical one.