Le, PhuongHo, Vu2022-01-262022-01-262018-03-15Le, P., & Ho, V. (2018). Stable solutions to weighted quasilinear problems of Lane-Emden type. <i>Electronic Journal of Differential Equations, 2018</i>(71), pp. 1-11.1072-6691https://hdl.handle.net/10877/15213We 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.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalQuasilinear problemsStable solutionsLane-Emden nonlinearityLiouville theoremsArticle