David, ArcoyaBoccardo, LucioLeonori, Tommaso2024-11-212024-11-212013-04-10Arcoya, D., Boccardo, L. & Leonori, T. -solutions for elliptic problems having gradient quadratic lower order terms. Nonlinear Differ. Equ. Appl. 20, 1741–1757 (2013). https://doi.org/10.1007/s00030-013-0228-z1420-9004; e-ISSN: 1021-9722https://doi.org/10.1007/s00030-013-0228-zhttps://hdl.handle.net/20.500.14468/24460In this paper we deal with solutions of problems of the type (Formula presented). where 0 < α ≤ a(x) ≤ β, {pipe}b(x){pipe} ≤ γ, γ > 0, f ∈ L2 (Ω) and Ω is a bounded subset of ℝN with N ≥ 3. We prove the existence of at least one solution for such a problem in the space W01,1 (Ω) ∩ L2 (Ω) if the size of the lower order term satisfies a smallness condition when compared with the principal part of the operator. This kind of problems naturally appears when one looks for positive minima of a functional whose model is: (Formula presented). where in this case a(x) ≡ b(x) = α > 0.eninfo:eu-repo/semantics/openAccess12 MatemáticasartículoNonlinear elliptic equationsW 1,1 0 (Ω) solutionsQuadratic gradient terms