Herrero, Miguel A.Velázquez, J.J. L.2023-06-202023-06-201991-010308-210510.1017/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