Chen, CaishengSong, HongxueYang, Hongwei2022-01-312022-01-312018-03-22Chen, C., Song, H., & Yang, H. (2018). Liouville-type theorems for stable solutions of singular quasilinear elliptic equations in R^N. <i>Electronic Journal of Differential Equations, 2018</i>(81), pp. 1-11.1072-6691https://hdl.handle.net/10877/15247We prove a Liouville-type theorem for stable solution of the singular quasilinear elliptic equations -div(|x|-αp |∇u|p-2 ∇u) = ƒ(x)|u|q-1u, in ℝN, -div(|x|-αp |∇u|p-2 ∇v) = ƒ(x)eu, in ℝN where 2 ≤ p < N, -∞ < α < (N - p)/p and the function ƒ(x) is continuous and nonnegative in ℝN \ {0} such that ƒ(x) ≥ c0|x|b as |x| ≥ R0, with b > -p(1 + α) and c0 > 0. The results hold for 1 ≤ p - 1 < q = qc(p, N, α, b) in the first equation, and for 2 ≤ N < q0(p, α, b) in the second equation. Here q0 and qc are exponents, which are always larger than the classical critical ones and depend on the parameters α, b.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalSingular quasilinear elliptic equationStable solutionsCritical exponentsLiouville type theoremsArticle