Liouville type theorems for stable solutions of p-Laplace equation in RN

In this paper we prove the Liouville type theorems for stable solution of the p-Laplace equations (0.1)−Δpu=f(x)eu,inRNand (0.2)Δpu=f(x)u−q,inRN,where 2≤p0 and the nonnegative function f(x)∈Lloc1(RN) such that f(x)≥c0|x|a as |x|≥R0 with a>−p and some constants R0,c0>0. The results hold true for 2≤N<μ0(p,a) in (0.1) and for q>qc(p,N,a) in (0.2). Here μ0 and qc are new exponents, which are always large than the classical critical ones and depend on the parameters p,a and N.