Liouville-type theorems for stable solutions of singular quasilinear elliptic equations in R^N
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Date
2018-03-22
Authors
Chen, Caisheng
Song, Hongxue
Yang, Hongwei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Singular quasilinear elliptic equation, Stable solutions, Critical exponents, Liouville type theorems
Citation
Chen, 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.
Rights
Attribution 4.0 International