Herrero, Miguel A.Velázquez, J.J. L.2023-06-202023-06-201991-01R. Bellman. Stability theory of differential equations (New York: Dover, 1953). H. Brezis. Semilinear equations in RN without conditions at infinity. Appl. Math. Optim. 12 (1984), 271-282. T. Gallouët and J. M. Morel. The equation -Δu + |u|α-1u = f for 0 ≤ α ≤ 1. J. Nonlinear Anal. 11 (1987), 893-912. M. A. Herrero and J. J. L. Velázquez. On the dynamics of a semilinear heat equation with strong absorption. Comm. Partial Differential Equations 14 (1989), 1653-1715. M. Murata. Structure of positive solutions to (-Δ + V)u=0 in RN. Duke Math J. 53 (1986), 869-943.0308-210510.1017/S0308210500029115https://hdl.handle.net/20.500.14352/57715We analyse the set of nonnegative, global, and radial solutions (radial solutions, for short) of the equation -Δu + u(p) = f in R(N), N ≥ 1, where 0 < p < 1, and f element-of L(loc)1(R(N)) is a radial and almost everywhere nonnegative function. We show that radial solutions of (E) exist if f(r) = o(r2p/1-p) or if f(r) ≈ cr2p/1-p as r --> ∞, where [GRAPHICS] When f(r) = c*r2p/1-p + h(r) with h(r) = o(r2p/1-p) as r --> ∞, radial solutions continue to exist if h(r) is sufficiently small at infinity. Existence, however, breaks down if h(r) > 0, [GRAPHICS] Whenever they exist, radial solutions are characterised in terms of their asymptotic behaviour as r --> ∞.engjournal articlehttp://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8244935http://journals.cambridge.orgopen access517.9EquationRNset of nonnegativeglobal and radial solutionsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias