Stable solutions to weighted quasilinear problems of Lane-Emden type
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Date
2018-03-15
Authors
Le, Phuong
Ho, Vu
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We prove that all entire stable W1,ploc solutions of weighted quasilinear problem
-div (w(x)|∇u|p-2 ∇u) = ƒ(x)|u|q-1u
must be zero. The result holds true for p ≥ 2 and p - 1 < q < qc(p, N, α, b). Here b > α - p and qc (p, N, α, b) is a new critical exponent, which is infinitely in low dimension and is always larger than the classic critical one, while w, ƒ ∈ L1loc(ℝN) are nonnegative functions such that w(x) ≤ C1|x|α and ƒ(x) ≥ C2|x|b for large |x|. We also construct an example to show the sharpness of our result.
Description
Keywords
Quasilinear problems, Stable solutions, Lane-Emden nonlinearity, Liouville theorems
Citation
Le, P., & Ho, V. (2018). Stable solutions to weighted quasilinear problems of Lane-Emden type. <i>Electronic Journal of Differential Equations, 2018</i>(71), pp. 1-11.