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Radial solutions of a semilinear elliptic problem*
Published online by Cambridge University Press: 14 November 2011
We analyse the set of nonnegative, global, and radial solutions (radial solutions, for short) of the equation
where 0 < p < 1, and is a radial and almost everywhere nonnegative function. We show that radial solutions of (E) exist if f(r) = o(r2p/1−1−p) or if f(r) ≈ cr2p/1−p as r → ∞, where
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,
Whenever they exist, radial solutions are characterised in terms of their asymptotic behaviour as r → ∞.
- Research Article
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 118 , Issue 3-4 , 1991 , pp. 305 - 326
- Copyright © Royal Society of Edinburgh 1991