Díaz Díaz, Jesús IldefonsoHernández, J.Rakotoson, Jean Michel Theresien2023-06-202023-06-2020111.H. Brezis, Une équation semi-linéaire avec conditions aux limites dans L 1, unpublished. Personal communication to J.I. Díaz. 2.Brezis H, Cazenave T, Martel Y, Raminandrisoa A.: Blow-up for u t − Δ u = g(u) revisited. Adv. Differential Equations 1, 72–90 (1996) 3.Brezis H, Strauss W.: Semilinear Elliptic Equations in L1. J. Math. Soc. Japan 25, 565–590 (1973) 4.Coclite M.M.: On a singular nonlinear Dirichlet problem II. Bolletino Unione Mat. Ital. B 5, 955–975 (1991) 5.Coclite M.M.: On a singular nonlinear Dirichlet problem III. Nonlinear Anal. 21, 547–564 (1993) 6.Coclite M.M.: On a singular nonlinear Dirichlet problem IV. Nonlinear Anal. 23, 925–936 (1994) 7.Crandall M.G, Rabinowitz P.H, Tartar L.: On a Dirichlet problem with singular nonlinearity. Comm. PDEs 2, 193–222 (1977) 8.del Pino M.: A global estimate for the gradient in a singular elliptic boundary value problem. Proc. Roy. Soc. Edinburgh 122, 341–352 (1992) 9.J.I. Díaz, J. Hernández and J.M. Rakotoson. On very weak positive solutions to some singular second order semilinear elliptic problems. In preparation. 10.Díaz J.I, Morel J.M, Oswald L.: An elliptic equation with singular nonlinearity. Comm. PDEs 12, 333–1344 (1987) 11.Díaz J.I., Rakotoson J.M.: On the differentiability of very weak solutions with righthand side data integrable with respect to the distance to the boundary. J. Funct. Anal. 357, 807–831 (2009) 12.Díaz J.I, Rakotoson J.M.: On very weak solutions of semilinear elliptic equations with right hand side data integrable with respect to the distance to the boundary. Discrete and Continuum Dynamical Systems 27, 1037–1058 (2010) 13.Ghergu M.: Lane-Emden systems with negative exponents. J. Functional Analysis 258, 3295–3318 (2010) 14.Gomes S.N.: On a singular nonlinear elliptic problem. SIAM J. Math. Anal. 17, 1259–1269 (1986) 15.Gui C, Hua Lin F.: Regularity of an elliptic problem with singular nonlinearity. Proc. Roy. Soc. Edinburgh 123, 1021–1029 (1993) 16.J. Hernández and F. Mancebo. Singular elliptic and parabolic equations. In Handbook of Differential equations (ed. M. Chipot and P. Quittner), vol. 3. Elsevier, 2006, 317-400. 17.Hernández J, Mancebo F, Vega J.M.: On the linearization of some singular, nonlinear elliptic problems and applications. Annls. Inst. H. Poincaré, Analyse non Linéaire 19, 777–813 (2002) 18.Hernández J, Mancebo F, Vega J.M.: Positive solutions for singular nonlinear elliptic equations. Proc. Roy. Soc. Edinburgh 137, 41–62 (2007) 19.Lazer A.C, McKenna P.J.: On a singular nonlinear elliptic boundary value problem. Proc. Amer. Math. Soc. 111, 721–730 (1991) 20.Mâagli H, Zbiri M.: Existence and estimates of solutions for singular nonlinear elliptic problems. J. Math. Anal. Appl. 263, 522–542 (2001) 21.Mâagli H, Zbiri M.: On a new Kato class and singular solutions of a nonlinear elliptic equation in bounded domains of R n . Positivity 9, 667–686 (2005) 22.Stuart C.A.: Existence and approximation of solutions of nonlinear elliptic equations. Math. Z. 147, 53–63 (1976) 23.Zhang Z, Cheng J.: Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems. Nonlinear Anal. 57, 473–484 (2004)1424-928610.1007/s00032-011-0151-xhttps://hdl.handle.net/20.500.14352/42140We use recent results by Diaz and Rakotoson concerning very weak solutions to linear boundary value problems in order to improve previous work on existence and properties of weak positive solutions to a model example of semilinear singular elliptic problem.engOn Very Weak Positive Solutions to Some Semilinear Elliptic Problems With Simultaneous Singular Nonlinear and Spatial Dependence Termsjournal articlehttp://www.springerlink.com/content/r17l23wm637r5483/fulltext.pdfhttp://www.springerlink.com/open access517.9Boundary-value problemdirichlet problemequationsexistenceNonlinear singular elliptic equationspositive very weak solutionsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias