RADIAL SOLUTIONS OF A SEMILINEAR ELLIPTIC PROBLEM

We analyse the set of nonnegative, global, and radial solutions (radial solutions, for short) of the equation -DELTA-u + u(p) = f in R(N), N greater-than-or-equal-to 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) almost-equal-to cr2p/1-p as r --> infinity, where [GRAPHICS] When f(r) = c*r2p/1-p + h(r) with h(r) = o(r2p/1-p) as r --> infinity, 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 --> infinity.