A nonexistence result for anisotropic problems*The authors are very grateful to the referee for his valuable remarks and suggestions, which helped us improve the paper. (9th November 2020) - Le, Phuong; Le, Kim Anh T; Dinh, Phuoc Vinh
Abstract: We study the anisotropic problem − ∑ i = 1 N ∂ ∂ x i ∂ u ∂ x i p i − 2 ∂ u ∂ x i = w f ( u ) in Ω, u = 0 on ∂ Ω, where p i ⩾ 2, Ω is a domain of R N, w is a nonnegative function and f is an increasing function. We prove that the problem has no nontrivial stable solution under various assumptions on p i, Ω, w and f .