Carmona, JoséLeonori, Tommaso2024-11-222024-11-222018-06-22Carmona, J., Leonori, T. ; A uniqueness result for a singular elliptic equation with gradient term (2018) Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148 (5), pp. 983-994. http://doi.org/10.1017/S03082105180001120308-2105, e-ISSN:1473-7124http://doi.org/10.1017/S0308210518000112https://hdl.handle.net/20.500.14468/24476We prove the uniqueness of a solution for a problem whose simplest model is with k ≥ 1, 0 Lz(Ω) and Ω is a bounded domain of N, N ≥ 2. So far, uniqueness results are known for k < 1, while existence holds for any k ≥ 1 and f positive in open sets compactly embedded in a neighbourhood of the boundary. We extend the uniqueness results to the k ≥ 1 case and show, with an example, that existence does not hold if f is zero near the boundary. We even deal with the uniqueness result when f is replaced by a nonlinear term λuq with 0 < q < 1 and λ > 0.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículocomparison principlenonlinear elliptic equationssingular natural growth gradient terms